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Finding Dense Submodules with Algebraic Lattice Reduction
We prove an algebraic analogue of Pataki-Tural lemma (Pataki-Tural, ar**v:0804.4014, 2008) – the main tool in analysing the so-called overstretched...
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Lattice-Valued Algebraic Structures Via Residuated Maps
It is proved recently that cuts of a lattice valued fuzzy set determine a residuated map from the codomain lattice to the power set of the domain...
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On the High Dimensional RSA Algorithm—A Public Key Cryptosystem Based on Lattice and Algebraic Number Theory
The most known public key cryptosystem was introduced in 1978 by Rivest et al. (1978) and is now called the RSA public key cryptosystem in their...
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On when the union of two algebraic sets is algebraic
In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize...
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Algebraic Structures Formalizing the Logic of Quantum Mechanics Incorporating Time Dimension
As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff...
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Topology of closure systems in algebraic lattices
Algebraic lattices are spectral spaces for the coarse lower topology. Closure systems in algebraic lattices are studied as subspaces. Connections...
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LATTICE VERTEX ALGEBRAS AND LOOP GRASSMANNIANS
For an integral symmetric matrix κ we construct a new “nonabelian homology localization” of the lattice vertex algebra
L κ on the corresponding loop... -
The Lattice Overparametrization Paradigm for the Machine Learning of Lattice Operators
The machine learning of lattice operators has three possible bottlenecks. From a statistical standpoint, it is necessary to design a constrained...
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On Algebraic Embedding for Unstructured Lattices
Lattice-based cryptography, the study of cryptographic primitives whose security is based on the hardness of so-called lattice problems, has taken...
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Lattice-Based Succinct Arguments from Vanishing Polynomials
Succinct arguments allow a prover to convince a verifier of the validity of any statement in a language, with minimal communication and verifier’s...
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Interactions with Lattice Polytopes Magdeburg, Germany, September 2017
This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes...
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An Algebraic View of the Mares-Goldblatt Semantics
An algebraic characterisation is given of the Mares-Goldblatt semantics for quantified extensions of relevant and modal logics. Some features of this...
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Lower Bounds for Lattice-Based Compact Functional Encryption
Functional encryption (FE) is a primitive where the holder of a master secret key can control which functions a user can evaluate on encrypted data....
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Lattice codes for lattice-based PKE
Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either trivial modulation or its concatenation with error...
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Representing Distributive Dually Algebraic Lattices
We show that every distributive dually algebraic lattice can be represented as Sp(S, H) with S an algebraic lattice and H a monoid of operators. As a...
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Algebraic Realizations of the Solutions for Three Quantum Mechanical Systems
Several quantum mechanical problems are studied all of which can be approached using algebraic means. The first problem introduces a large class of...
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Random Algebraic Numbers
A family of measures on a given set of real algebraic numbers of arbitrary fixed degree is considered. The paper presents a method for constructing a...
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Hodge similarities, algebraic classes, and Kuga–Satake varieties
We introduce in this paper the notion of Hodge similarities of transcendental lattices of hyperkähler manifolds and investigate the Hodge conjecture...
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Lattice-Based Cryptography: A Survey
Most of current public key cryptosystems would be vulnerable to the attacks of the future quantum computers. Post-quantum cryptography offers...