Construction Of Class Research Articles

Deep autoencoders for physics-constrained data-driven nonlinear materials modeling

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains difficult to deal with high-dimensional applications and extrapolative generalization. This paper introduces deep learning techniques under the data-driven framework to address these fundamental issues in nonlinear materials modeling. To this end, an autoencoder neural network architecture is introduced to learn the underlying low-dimensional representation (embedding) of the given material database. The offline trained autoencoder and the discovered embedding space are then incorporated in the online data-driven computation such that the search of optimal material state from database can be performed on a low-dimensional space, aiming to enhance the robustness and predictability with projected material data. To ensure numerical stability and representative constitutive manifold, a convexity-preserving interpolation scheme tailored to the proposed autoencoder-based data-driven solver is proposed for constructing the material state. In this study, the applicability of the proposed approach is demonstrated by modeling nonlinear biological tissues. A parametric study on data noise, data size and sparsity, training initialization, and model architectures, is also conducted to examine the robustness and convergence property of the proposed approach.

On the integral domains characterized by a Bezout property on intersections of principal ideals

In this article we study two classes of integral domains. The first is characterized by having a finite intersection of principal ideals being finitely generated only when it is principal. The second class consists of the integral domains in which a finite intersection of principal ideals is always non-finitely generated except in the case of containment of one of the principal ideals in all the others. We relate these classes to many well-studied classes of integral domains, to star operations and to classical and new ring constructions.

Nonproper intersection products and generalized cycles

We develop intersection theory in terms of the {{mathscr {B}}}-group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct images of Chern forms and it contains all usual cycles. However, contrary to Chow classes, the {{mathscr {B}}}-classes have well-defined multiplicities at each point. We focus on a {{mathscr {B}}}-analogue of the intersection theory based on the Stückrad–Vogel procedure and the join construction in projective space. Our approach provides global {{mathscr {B}}}-classes which satisfy a Bézout theorem and have the expected local intersection numbers. We also introduce {{mathscr {B}}}-analogues of more classical constructions of intersections using the Gysin map of the diagonal. These constructions are connected via a {{mathscr {B}}}-variant of van Gastel’s formulas. Furthermore, we prove that our intersections coincide with the classical ones on cohomology level.

A Flow Analysis Using a Water Tunnel of an Innovative Unmanned Aerial Vehicle

The purpose of this article is to present and discuss the results of a non-standard unnamed aerial vehicle construction with a constant cross-section square-shaped avionic profile. Based on the model’s in-air observed maneuverability, the research of avionic construction behavior was carried out in a water tunnel. The results show the model’s specific lift capabilities in comparison to classical avionic constructions. The characteristic results of the lift coefficient showed that the unmanned aerial vehicle presents favorable features than classic avionic constructions. The model was created with the prospect of using it in the future for dual-use purposes, where unmanned aerial vehicles are currently experiencing very rapid development. When creating the prototype, the focus was on low production cost, as well as convenience in operation. The development of this type of breakthrough avionic solution, which shows extraordinary maneuverability, may contribute to increasing the popularity and, above all, the availability of unmanned aerial vehicles for the largest possible group of recipients because of high avionic properties in relation to the technical construction complexity.

A Homological Casson Type Invariant of Knotoids

We consider an analogue of the well-known Casson knot invariant for knotoids. We start with a direct analogue of the classical construction which gives two different integer-valued knotoid invariants and then focus on its homology extension. The value of the extension is a formal sum of subgroups of the first homology group $$H_1(\varSigma )$$ where $$\varSigma $$ is an oriented surface with (maybe) non-empty boundary in which knotoid diagrams lie. To make the extension informative for spherical knotoids it is sufficient to transform an initial knotoid diagram in $$S^2$$ into a knotoid diagram in the annulus by removing small disks around its endpoints. As an application of the invariants we prove two theorems: a sharp lower bound of the crossing number of a knotoid (the estimate differs from its prototype for classical knots proved by M. Polyak and O. Viro in 2001) and a sufficient condition for a knotoid in $$S^2$$ to be a proper knotoid (or pure knotoid with respect to Turaev’s terminology). Finally we give a table containing values of our invariants computed for all spherical prime proper knotoids having diagrams with at most 5 crossings.

About some incredible adventures of the “elusive” duty construction

The article gives “biographies” of the construction of duty in atypical situations. The first of them is illustrated by the example of family legal relations between parents and children, in which parents are at the same time responsibilities for upbringing (the structure of right-duty). The doctrine accepts such a feature of the aforementioned type of legal relationship by no means to everyone - a reference to the classical interaction of the pair “right and duty” and their distribution between the subject. An additional argument is the arguments in favor of the child’s incapacity and, consequently, the inadmissibility of imposing any responsibilities on him. As counterarguments, considerations are expressed about the possibility of the existence of exceptions from classical constructions, as well as about the presence of certain elements of legal capacity in the child, which make it possible to assign certain responsibilities to him, including in relation to parents or persons substituting for them. As additional argumentation, examples are given of assigning children of different ages (6, 10, 14 years) to responsibilities in the field of education, family, civil turnover. It is proposed to provide for the obligation of children to respect their parents in the general principles of family law. The second atypical situation arises when the so-called declarative obligations are fixed in the text of the law. It is emphasized that they, either directly or indirectly, are associated with certain legal consequences of their non-compliance, therefore, they possess, albeit not in the classical execution, the properties of a legal obligation.

Uniqueness of billiard coding in polygons

We consider polygonal billiards and we show that every nonperiodic billiard trajectory hits a unique sequence of sides if all the holes of the polygonal table have non-zero minimal diameters, generalizing a classical theorem of Galperin, Krüger and Troubetzkoy. Our approach uses symbolic dynamics and elementary geometry. We review some classical constructions in polygonal billiards and we introduce, as one of our main tools, a method to code pairs of parallel billiard trajectories in non-simply connected polygons. We also discuss some useful properties of ‘generalized trajectories’, which can be uniquely constructed from the limits of converging sequences of billiard codings.

Twistor spaces on foliated manifolds

The theory of twistors on foliated manifolds is developed. We construct the twistor space of the normal bundle of a foliation. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate and prove foliated versions of some well-known results on holomorphic mappings. Since any orbifold can be understood as the leaf space of a suitably defined Riemannian foliation we obtain orbifold versions of the classical results as a simple consequence of the results on foliated mappings.

Resolution \xe0 la Kronheimer of mathbb {C}^3/Gamma singularities and the Monge\u2013Amp\xe8re equation for Ricci-flat K\xe4hler metrics in view of D3-brane solutions of supergravity

In this paper, we analyze the relevance of the generalized Kronheimer construction for the gauge/gravity correspondence. We begin with the general structure of D3-brane solutions of type IIB supergravity on smooth manifolds Y^Gamma that are supposed to be the crepant resolution of quotient singularities mathbb {C}^3/Gamma with Gamma a finite subgroup of SU(3). We emphasize that nontrivial 3-form fluxes require the existence of imaginary self-dual harmonic forms omega ^{2,1}. Although excluded in the classical Kronheimer construction, they may be reintroduced by means of mass deformations. Next we concentrate on the other essential item for the D3-brane construction, namely, the existence of a Ricci-flat metric on Y^Gamma . We study the issue of Ricci-flat Kähler metrics on such resolutions Y^Gamma , with particular attention to the case Gamma =mathbb {Z}_4. We advance the conjecture that on the exceptional divisor of Y^Gamma the Kronheimer Kähler metric and the Ricci-flat one, that is locally flat at infinity, coincide. The conjecture is shown to be true in the case of the Ricci-flat metric on mathrm{tot} K_{{mathbb {W}P}[112]} that we construct, i.e., the total space of the canonical bundle of the weighted projective space {mathbb {W}P}[112], which is a partial resolution of mathbb {C}^3/mathbb {Z}_4. For the full resolution, we have Y^{mathbb {Z}_4}={text {tot}} K_{mathbb {F}_{2}}, where mathbb {F}_2 is the second Hirzebruch surface. We try to extend the proof of the conjecture to this case using the one-parameter Kähler metric on mathbb {F}_2 produced by the Kronheimer construction as initial datum in a Monge–Ampère (MA) equation. We exhibit three formulations of this MA equation, one in terms of the Kähler potential, the other two in terms of the symplectic potential but with two different choices of the variables. In both cases, one can establish a series solution in powers of the variable along the fibers of the canonical bundle. The main property of the MA equation is that it does not impose any condition on the initial geometry of the exceptional divisor, rather it uniquely determines all the subsequent terms as local functionals of this initial datum. Although a formal proof is still missing, numerical and analytical results support the conjecture. As a by-product of our investigation, we have identified some new properties of this type of MA equations that we believe to be so far unknown.

Structured discrete shape approximation: Theoretical complexity and practical algorithm

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and orientation restrictions. We show that already deciding feasibility of such approximation problems is NP-hard, and remains intractable even for very simple setups. We then devise an algorithmic framework that combines shape sampling with exact cardinality minimization to obtain good approximations using few components. As a particular application and showcase example, we discuss approximating shape contours using the classical Zometool construction kit and provide promising computational results, demonstrating that our algorithm is capable of obtaining good shape representations within reasonable time, in spite of the problem's general intractability. We conclude the paper with an outlook on possible extensions of the developed methodology, in particular regarding 3D shape approximation tasks.

A non-Archimedean analogue of Teichm\xfcller space and its tropicalization

In this article we use techniques from tropical and logarithmic geometry to construct a non-Archimedean analogue of Teichmüller spaceoverline{{{mathcal {T}}}}_g whose points are pairs consisting of a stable projective curve over a non-Archimedean field and a Teichmüller marking of the topological fundamental group of its Berkovich analytification. This construction is closely related to and inspired by the classical construction of a non-Archimedean Schottky space for Mumford curves by Gerritzen and Herrlich. We argue that the skeleton of non-Archimedean Teichmüller space is precisely the tropical Teichmüller space introduced by Chan–Melo–Viviani as a simplicial completion of Culler–Vogtmann Outer space. As a consequence, Outer space turns out to be a strong deformation retract of the locus of smooth Mumford curves in overline{{mathcal {T}}}_g.

Random walks on groups and KMS states

A classical construction associates to a transient random walk on a discrete group \(\Gamma \) a compact \(\Gamma \)-space \(\partial _M \Gamma \) known as the Martin boundary. The resulting crossed product \(C^*\)-algebra \(C(\partial _M \Gamma ) \rtimes _r \Gamma \) comes equipped with a one-parameter group of automorphisms given by the Martin kernels that define the Martin boundary. In this paper we study the KMS states for this flow and obtain a complete description when the Poisson boundary of the random walk is trivial and when \(\Gamma \) is a torsion free non-elementary hyperbolic group. We also construct examples to show that the structure of the KMS states can be more complicated beyond these cases.

Geopolymers made from metakaolin sources, partially replaced by Spanish clays and biomass bottom ash

The main objective of this investigation is to study the effect of the substitution of metakaolin (MK) (from calcined industrial kaolin) by four different calcined natural Southern Spain clays traditionally used in the brick and tile sector, as well as by the biomass bottom ash residue (BBA) from the combustion of a mix of olive and pine pruning on the synthesis of geopolymer with physical, mechanical and thermal properties comparable to those of classic construction materials. As alkaline activator, a 8 M solution of sodium hydroxide and sodium silicate have been used. Raw materials, metakaolin; Spanish clays: black clay (BC), yellow clay (YC), white clay (WC), red clay (RC) and BBA were characterized by chemical analysis (XRF), mineralogical analysis (XRD), and particle size analysis. Control geopolymers containing only metakaolin, and batch of geopolymers were formulated containing equal proportions of metakaolin, BBA and each of the four types of clay. After the curing period, at 60 °C for 1 day geopolymers were demolded and stored 27 days at room temperature. Geopolymers were characterized using Scanning Electron Microscopy coupled with Energy Dispersive Spectroscopy (SEM-EDS), XRD and Attenuated Total Reflectance- Fourier Transform Infrared Spectroscopy (ATR-FTIR). Their physical, mechanical and thermal properties have also been studied. The addition of BBA and different types of calcined clays to metakaolin gives rise to geopolymers with higher mechanical properties increasing the compressive strength of the control geopolymer containing only MK (24.9 MPa) by more than 50% for the GMK-BBA-WC geopolymers (38.5 MPa). The clays act as fillers and/or promote the precipitation of calcium-rich phases (Ca)-A-S-H-G gel that coexists with the (Na)-A-S-H gel type. The relevant results of physical, mechanical and thermal properties obtained in this research demonstrate the potential of Spanish clays and BBA as binders and substitutes for metakaolin.

Explicit Two-Deletion Codes With Redundancy Matching the Existential Bound

We give an explicit construction of length- n binary codes capable of correcting the deletion of two bits that have size 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> /n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+o(1)</sup> . This matches up to lower order terms the existential result, based on an inefficient greedy choice of codewords, that guarantees such codes of size Ω(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> /n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ). Our construction is based on augmenting the classic Varshamov-Tenengolts construction of single deletion codes with additional check equations. We also give an explicit construction of binary codes of size Ω(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> /n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+o(1)</sup> ) that can be list decoded from two deletions using lists of size two. Previously, even the existence of such codes was not clear.

Generalized and graded geometry for mechanics: a comprehensive introduction

In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of classical differential geometric constructions in the context can be conveniently described using the language of Q-structures, and thus Q-structure preserving integrators are potentially of great use in mechanics. We give some hints how the latter can be constructed, and formulate some open problems. Since the text is intended both to mathematics and mechanics communities, we tried to make it accessible to non-geometers as well.

Real algebraic curves of bidegree (5,5) on the quadric ellipsoid

We complete the topological classification of real algebraic non-singular curves of bidegree $(5, 5)$ on the quadric ellipsoid. We show in particular that previously known restrictions form a complete system for this bidegree. Therefore, the main part of the paper concerns the construction of real algebraic curves. Our strategy is first to reduce to the construction of curves in the second Hirzebruch surface by degenerating the quadric ellipsoid to the quadratic cone. Next, we combine different classical construction methods on toric surfaces, such as Dessin d'enfants and and Viro's patchworking method.

Construction and Applications of Stairboxplot for Exploratory Data Analysis

The classical construction of boxplot requires estimates of five robust statistics of interest namely, the first quartile, the median, the third quartile, the lower fence and the upper fence. The fence estimate is usually dependent on the three quartiles and is utilized to visually identify outliers in a batch of univariate dataset. Some scholars are critical of the limitation of boxplox to display individual data points, density of observations and distributional shape in multiple batch comparison among to mention. In this paper display enhancement to address the limitations of classical boxplot is proposed according to a new construction method called stairboxplot. The construction begins with display of four stairs of consecutive boxes according to quadbins to replace box and whiskers in the classical boxplot construction and an inscription of individual observations using scale adjusted outlyingness estimate of each data point. The advantage of stairboxplot as a data display toolkit was explored using simulation and real life dataset.

A Review on the Energy Performance and Efficiency of Radiant Floor Heating Systems with Integrated Phase Change Materials

Abstract In the modern society the concept of energy efficiency of buildings has become a subject of great interest, due to the negative impact of buildings upon the environment, society and economy. One of the methods of overcoming this is to provide a better efficiency of the energy storage because it is the key to resolve the difference between supply and demand. In comparison to electro-chemical batteries which provide limited energy storage at a high financially cost, thus in this regard, thermal energy storage technologies with high energy density have increased market potential. PCMs present objective advantages in comparison to classic construction materials due to their characteristics of being able to store and release higher quantities of thermal energy during the phase change process. A PCM radiant floor heating system can provide a reduction of the energy consumption for heating by up to 43%, trough the higher discharge time of the PCM compared to regular heating systems.

UNITY and B\xfcchi automata

UNITY is a model for concurrent specifications with a complete logic for proving progress properties of the form “P leads to Q”. UNITY is generalized to U-specifications by giving more freedom to specify the steps that are to be taken infinitely often. In particular, these steps can correspond to non-total relations. The generalization keeps the logic sound and complete. The paper exploits the generalization in two ways. Firstly, the logic remains sound when the specification is extended with hypotheses of the form “F leads to G”. As the paper shows, this can make the logic incomplete. The generalization is used to show that the logic remains complete, if the added hypotheses “F leads to G” satisfy “F unless G”. The main result extends the applicability and completeness of UNITY logic to proofs that a given concurrent program satisfies any given formula of LTL, linear temporal logic, without the next-operator which is omitted because it is sensitive to stuttering. For this purpose, the program, written as a UNITY program, is extended with a number of boolean variables. The proof method relies on implementing the LTL formula, i.e., restricting the specification in such a way that only those runs remain that satisfy the formula. This result is a variation of the classical construction of a Büchi automatonfor a given LTL formula that accepts precisely those runs that satisfy the formula.

Comparison and Analysis of Network Construction Methods for Seismicity Based on Complex Networks

The approach of the complex network has well described seismic complex systems. In this paper, this is the first time three classical network construction methods for seismicity are compared. By using the same dataset from the Southern California Seismic Network, three networks are constructed. They all present the scale-free, small-world properties, a strength-degree correlation, and an assortative mixing feature. However, they show some differences in the hierarchical clustering feature. On observing the evolution results, three measures show a similar correlation with seismicity dynamics, but one measure shows a different result. These results show that different network construction methods will present some similarities and differences in network properties. This situation needs to be considered, especially when discussing a predictive indicator of seismicity.