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We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies' wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. In particular, lattice fields are identified with the continuum field smeared with Daubechies' scaling functions. We compare our scaling maps with other renormalization schemes and their features, such as the momentum shell method or block-spin transformations., Comment: 66 pages, 4 figure (accepted version)

Let L denote the Q-lattice of the variety $${\mathcal {V}}$$ of lattices, i.e. the lattice of quasivarieties that are contained in $${\mathcal {V}}$$ . Let F denote the free lattice in $${\mathcal {V}}$$ with $$\omega $$ free generators and let Q(F) denote the quasivariety of lattices generated by F. Let Fin denote the collection of finite lattices which belong to Q(F) and let Q(Fin) denote the quasivariety generated by Fin. Moreover, let $${\mathcal {M}}^{-}_{3}$$ denote the quasivariety of lattices which do not contain an isomorphic copy of $$M_3$$ (the 5-element non-distributive modular lattice) as a sublattice and let $${\mathcal {S}}$$ denote a selector of non-isomorphic finite quasicritical lattices which belong to Q(Fin). In this paper, we establish the following

As most of the published lattice based encryptions and key encapsulation mechanisms have decryption failure, they are subjected to side-channel attacks. In this paper, we construct an error-free lattice-based key encapsulation mechanism (KEM) which is based on LPR encryption. We also examine some new classes of cyclotomic polynomials for the new error-free lattice-based KEM. The proposed error-free KEM has a reasonable public key size of about 1.472 Kbytes for 128-bit quantum security level. This is comparable to those submitted to the NIST PQC standardization.

We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer, rephrased in terms of quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional grid, keeping the same computational advantage with respect to the classical algorithms. For this purpose, we have considered the free lattice Hamiltonian, with linear dispersion relation introduced by Childs and Ge The numerical simulations showed that the walker finds the marked vertex in O(N1/4log3/4N) steps, with probability O(1/logN), for an overall complexity of O(N1/4log5/4N), using amplitude amplification. We also proved that there exists an optimal choice of the walker parameters to avoid the time measurement precision affecting the complexity searching time of the algorithm.

Physics letters / B 809, 135713 (2020). doi:10.1016/j.physletb.2020.135713, We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (Möbius) domain-wall fermion in 1+1 dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of N≥3 , the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in Möbius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size., Published by North-Holland Publ., Amsterdam

We show that there is no distributive law of the free lattice monad over the powerset monad. The proof presented here also works for other classes of lattices such as (bounded) distributive/modular lattices and also for some variants of the powerset monad such as the (nonempty) finite powerset monad.

The problem of determining (up to lattice isomorphism) the lattices that are sublattices of free lattices is in general an extremely difficult and an unsolved problem. A notable result towards solving this problem was established by Galvin and Jonsson when they classified (up to lattice isomorphism) all of the distributive sublattices of free lattices in 1959. In this paper, we weaken the requirement that a sublattice of a free lattice be distributive to requiring that a such a lattice belongs in the variety of lattices generated by the pentagon $$N_5$$ . Specifically, we use McKenzie’s list of join-irreducible covers of the variety generated by $$N_5$$ to extend Galvin and Jonsson’s results by proving that all sublattices of a free lattice that belong to the variety generated by $$N_5$$ satisfy three structural properties. Afterwards, we explain how the results in this paper can be partially extended to lattices from seven known infinite sequences of semidistributive lattice varieties.

Concept lattices and closed set lattices are graphs with the lattice property. They have been increasingly used this last decade in various domains of computer science, such as data mining, knowledge representation, databases or information retrieval. A fundamental result of lattice theory establishes that any lattice is the concept lattice of its binary table. A consequence is the existence of a bijective link between lattices, contexts (via the table) and a set of implicational rules (via the canonical (direct) basis). The possible transformations between these objects give rise to relevant tools for data analysis. In this paper, we present a survey of lattice theory, from the algebraic definition of a lattice, to that of a concept lattice, through closure systems and implicational rules; including the exploration of fundamental bijective links between lattices, reduced contexts and bases of implicational rules; and concluding with the presentation of the main generation algorithms of these objects.

We consider the macroscopic system of free lattice fermions in one dimensions assuming that the one-body Hamiltonian of the system is the one dimensional discrete Schr\"odinger operator with independent identically distributed random potential. We show that the variance of the entanglement entropy of the segment $[-M,M]$ of the system is bounded away from zero as $% M\rightarrow \infty $. This manifests the absence of the selfaveraging property of the entanglement entropy in our model, meaning that in the one-dimensional case the complete description of the entanglement entropy is provided by its whole probability distribution. This also may be contrasted the case of dimension two or more, where the variance of the entanglement entropy per unit surface area vanishes as $M\rightarrow \infty $ \cite{El-Co:17}, thereby guaranteing the representativity of its mean for large $M$ in the multidimensional case.

Additive Manufacturing (AM) has become more relevant to industry in recent years and enables fabrication of complex lightweight lattice structures. Nevertheless, material extrusion processes require internal and/or external support structures for the printing process. These support structures generate costs due to additional material, printing time and energy.

Always-on spoken language interfaces, e.g. personal digital assistants, rely on a wake word to start processing spoken input. We present novel methods to train a hybrid DNN/HMM wake word detection system from partially labeled training data, and to use it in on-line applications: (i) we remove the prerequisite of frame-level alignments in the LF-MMI training algorithm, permitting the use of un-transcribed training examples that are annotated only for the presence/absence of the wake word; (ii) we show that the classical keyword/filler model must be supplemented with an explicit non-speech (silence) model for good performance; (iii) we present an FST-based decoder to perform online detection. We evaluate our methods on two real data sets, showing 50%--90% reduction in false rejection rates at pre-specified false alarm rates over the best previously published figures, and re-validate them on a third (large) data set., Comment: Accepted at Interspeech 2020. 5 pages, 3 figures

We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a monopole-anti-monopole pair of magnetic charge $\pm Q$ separated by a distance $s$ in a periodic $L^3$ lattice, and study the low-lying eigenvalues of different lattice Dirac operators under a continuum limit defined by taking $L\to\infty$ at fixed $s/L$. As the background gauge field is parity even, we look for a two-fold degeneracy of the Dirac spectrum that is expected of a continuum-like Dirac operator. The naive-Dirac operator exhibits such a parity-doubling, but breaks the degeneracy of the fermion-doubler modes for the $Q$ lowest eigenvalues in the continuum limit. The Wilson-Dirac operator lifts the fermion-doublers but breaks the parity-doubling in the $Q$ lowest modes even in the continuum limit. The overlap-Dirac operator shows parity-doubling of all the modes even at finite $L$ that is devoid of fermion-doubling, and singles out as a properly regulated continuum Dirac operator in the presence of singular gauge field configurations albeit with a peculiar algorithmic issue., 21 pages, 9 figures

Enumerating all the spanning trees of a complex network is theoretical defiance for mathematicians, electrical engineers and computer scientists. In this article, we propose a generalization of the Fractal Scale-Free Lattice and we study its structural properties. As its degree distribution follows a power law, we prove that the proposed generalization does not affect the scale-free property. In addition, we use the electrically equivalent transformations to count the number of spanning trees in the generalized Fractal Scale-Free Lattice. Finally, in order to evaluate the robustness of the generalized lattice, we compute and compare its entropy with other complex networks having the same average degree.

We investigate when fiber products of lattices are finitely generated and obtain a new characterization of bounded lattice homomorphisms onto lattices satisfying a property we call Dean’s condition (D) which arises from Dean’s solution to the word problem for finitely presented lattices. In particular, all finitely presented lattices and those satisfying Whitman’s condition satisfy (D). For lattice epimorphisms [Formula: see text], [Formula: see text], where [Formula: see text], [Formula: see text] are finitely generated and [Formula: see text] satisfies (D), we show the following: If [Formula: see text] and [Formula: see text] are bounded, then their fiber product (pullback) [Formula: see text] is finitely generated. While the converse is not true in general, it does hold when [Formula: see text] and [Formula: see text] are free. As a consequence, we obtain an (exponential time) algorithm to decide boundedness for finitely presented lattices and their finitely generated sublattices satisfying (D). This generalizes an unpublished result of Freese and Nation.

Recently, several algorithms for strain tomography from energy-resolved neutron transmission measurements have been proposed. These methods assume that the stress-free lattice spacing $d_0$ is a known constant limiting their application to the study of stresses generated by manufacturing and loading methods that do not alter this parameter. In this paper, we consider the more general problem of jointly reconstructing the strain and $d_0$ fields. A method for solving this inherently non-linear problem is presented that ensures the estimated strain field satisfies equilibrium and can include knowledge of boundary conditions. This method is tested on a simulated data set with realistic noise levels, demonstrating that it is possible to jointly reconstruct $d_0$ and the strain field., Journal article, 14 pages, 5 figures

The study is aimed at developing a modular lattice base for automatic food machines, starting with a solution already patented by some of the authors. In this case, welded carpentry modules were interlocked with a system of profiles and metal inserts, also in welded carpentry, and the union was stabilized by structural adhesive bonding. Since welding involves long processing times and thermal distortions to be restored later, the driver of this study is to limit the use of welding as much as possible while increasing the modularity of the construction. For this purpose, various solution concepts have been generated where a common feature is the presence of rods of the same geometry and section to be joined together in configurable structural nodes. The concepts are qualitatively evaluated in light of the requirements, and the selected concept is digitally and physically prototyped. The prototype has been in service from over 5 years without showing any problems whatsoever.

We study the temporal evolution of the entanglement hamiltonian of an interval after a global quantum quenchin free lattice models in one spatial dimension. In a harmonic chain we explore a quench of the frequency parameter. In a chain of free fermions at half filling we consider the evolution of the ground state of a fully dimerised chain through the homogeneous hamiltonian. We focus on critical evolution hamiltonians. The temporal evolutions of the gaps in the entanglement spectrum are analysed. The entanglement hamiltonians in these models are characterised by matrices that provide also contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench., 68 pages, 25 figures. v2: improved analysis of the fermionic quench, published version