Toric geometry of path signature varieties

In stochastic analysis, a standard method to study a path is to work with its signature. This is a sequence of tensors of different order that encode information of the path in a compact form. When the path varies, such signatures parametrize an algebraic variety in the tensor space. The study of these signature varieties builds a bridge between algebraic geometry and stochastics, and allows a fruitful exchange of techniques, ideas, conjectures and solutions. In this paper we study the signature varieties of two very different classes of paths. The class of rough paths is a natural extension of the class of piecewise smooth paths. It plays a central role in stochastics, and its signature variety is toric. The class of axis-parallel paths has a peculiar combinatoric flavour, and we prove that it is toric in many cases.Comment: Code for the computations is available at https://sites.google.com/view/l-colmenarejo/publications/cod

Enhanced Effective Thickness of Multi-Layered Laminated Glass

The stiffness and strength of laminated glass, a composite of glass layers bonded together by polymeric interlayers, depend upon shear coupling between the glass plies through the polymer. In the design practice, this effect is commonly considered by defining the effective thickness, i.e., the thickness of a monolith with equivalent bending properties. Traditional formulations have been proposed for a package of two layers of glass and one polymeric interlayer, but their extrapolation to a higher number of layers gives in general inaccurate results. Here, the recently-proposed Enhanced Effective Thickness method is extended to the case of laminated glass beams composed i) by three layers of glass of arbitrary thickness, or ii) by an arbitrary number of equally-thick glass layers. Comparison with numerical experiments confirms the accuracy of the proposed approach

Composite beams with viscoelastic interaction. An application to laminated glass.

A practical way to calculate the response of laminated glass is to consider both glass and polymeric interlayer as linear elastic materials; the viscoelastic behavior of the polymer is evaluated assuming equivalent elastic moduli, that is, the relaxed moduli under constant strain after a time equal to the duration of the design action. Here, we analytically solve the time-dependent problem of simply-supported laminated-glass beams, modeling the response of the polymer by a Prony’s series of Maxwell elements. The obtained results, in agreement with a full 3-D viscoelastic finite-element numerical analysis, emphasize that there is a noteworthy difference between the state of strain and stress calculated in the full-viscoelastic case or in the aforementioned “equivalent” elastic problem. The second approach gives in general results that are on the side of safeness, but the design may be too conservative for short-time actions, whose duration depends upon the polymer type

Effective Thickness of Laminated Glass Beams.New expression via a variational approach.

The performance of laminated glass, which consists of two or more glass plies bonded together by polymeric interlayers, depends upon shear coupling between the plies through the polymer. This is commonly considered by defining the effective thickness, i.e., the thickness of a monolithic beam with equivalent bending properties in terms of stress and deflection. General expressions have been proposed on the basis of simplified models by Newmark and Wölfel-Bennison, but they are either diffcult to apply or inaccurate. Here, a variational approach to the problem is presented. By choosing appropriate shape functions for the laminated-beam deformation, minimization of the strain energy functional gives new expressions for the effective thickness under any constraint- and load-conditions, embracing the classical formulations as particular cases. Comparisons with numerical experiments confirm the better accuracy of the proposed approach with respect to the previous ones

Post-breakage Tensile and Bending Response of Laminated Glass

Laminated glass, composed by glass plies sandwiching polymeric interlayers, can provide a safe post-glass breakage response, in compliance with the fail-safe approach used in the structural design. In fact, when glass breaks, shards remain attached to the polymer, preventing danger from falling materials and imparting a "tension stiffening" effect to the interlayer, so that the broken panel maintains a certain residual load-bearing capacity. Here, a homogenized approach is presented to describe the mechanical properties of broken heat-treated laminated glass under tensile stresses. The model accounts for the stress diffusion from the delaminated zones, where shards are bridged by the interlayer-ligament only, to the regions where glass is bonded to the interlayer. The model provides a simple but accurate estimate of the effective tensile properties of the cracked laminate. Here, the influence of the interlayer thickness, the size of the glass shards and the glass-polymer delamination on the post-critical response is accurately investigated, and analytical results are compared with numerical ones. The obtained expression for the tensile modulus is used to predict, in more general terms, the response of cracked laminated glass under in-plane and out-of-plane bending. In both cases, a key point is the correct evaluation of the tension stiffening in the polymeric interlayer due to the adhesion with the glass shards

Practical expressions for the design of laminated glass

Due to deformability of the polymeric interlayer, stiffness and strength of laminated glass are usually less than those corresponding to a monolith with same total thickness. A practical design tool consists in the definition of the “effective thickness”, i.e., the thickness of an equivalent monolithic glass that would correspond to the same deflection and peak stress of the laminated glass, under the same constraint and load conditions. Very recently, a new model has been proposed for the evaluation of the effective thickness. Here, a comparison is made with the classical approach by Wölfel-Bennison and the new method is specialized to the most common cases of the design practice, providing synthetic tables for ease of reference and immediate applicability

Sharing of general loading in double glazed units. The BAM analytical approach

Double Glazed Units (DGUs) consist of two glass panes held together by structural edge seals. Calculation methods for DGUs consider that actions applied on one pane develop effects in all the panes, due to the coupling from the entrapped gas. Various methods have been proposed in standards to evaluate this load sharing, which depends upon the stiffness of the glass panes, the thicknesses of spacer and the size of the DGU. A comprehensive analytical formulation, the Betti’s Analytical Method (BAM), has been recently proposed to calculate the load sharing in DGUs of any shape, composed by glass panes of arbitrary thickness, with various support conditions at the borders and various types of external actions, including concentrated and line loads. Simple expressions can determine the gas pressure as a function of a universal shape function, which coincides with the deformed surface of a simply supported plate, of the same shape of the DGU, under uniformly distributed load. Here, comparisons are made with numerical analyses, performed by implementing an ad hoc routine in the software Straus7, developed by Maffeis Engineering, where the deflection of the glass panels is iteratively calculated, until the volume enclosed reaches a value compatible with the pressure exerted by the gas. The numerical routine, that is part of an integrated parametric approach to the façades design, allows precise calculations for any kind of build-up, panel shapes and load conditions

Prevalence and risk factors associated with cat parasites in Italy: a multicenter study

Background: Parasites that infect cats include protozoa, helminths and arthropods, many of which are transmissible to humans. Effective control relies on a good knowledge of parasite distribution and the risk factors for infection. The present study was aimed at evaluating the prevalence of major feline parasites in Italy and the risk factors associated with their occurrence. Methods: Over a 12-month study period, feces, hair and ectoparasites from naturally infected cats from feral colonies, shelters and private households were analyzed at 13 study centers across Italy. Samples from these cats (n = 987) were analyzed at all centers using the same diagnostic methods. Prevalence values and risk factors were evaluated statistically for the identification of predictors of risk. Results: The overall prevalence of gastro-intestinal and broncho-pulmonary (BP) nematodes was 35.9% (354/987). Toxocara cati was the most prevalent species (253/987; 25.6%), followed by Ancylostomatidae (98/987; 9.9%). Among BP nematodes, Aelurostrongylus abstrusus was the most common (76/987; 7.7%). Approximately 35.7% (352/987) of the study population was infested by ectoparasites, of which the most common were fleas (29.4%, 290/987), followed by ear mites Otodectes cynotis (9.8%, 97/987). Predictors of risk for parasite infection included age, a predominantly or exclusively outdoor lifestyle, geographic area and lack of antiparasitic treatment. Conclusions: Both ecto- and endoparasites are still common in cats throughout Italy, many of them being of zoonotic concern and vectors of pathogens to humans. Given the presence of parasites throughout the entire study period, year-round treatment should be considered. Furthermore, data confirm the need to protect the human–animal bond using proper endo- and ectoparasiticides to reduce the risk of human infection, in application of the One-Health concept

Determining equivalent-sectional shear modulus in torsion tests for laminated glass beams using photogrammetry method

This paper proposes a concise concept for quantifying the shear/torsional stiffness of the laminated glass beams experimentally by introducing the Equivalent-Sectional Shear Modulus (ESSM), that is directly measured from the torque and sectional-rotation correlation with the torsion test and tailor-made photogrammetry technique. The advantage of this method is originated from the concept of measuring the overall rotation to torque response of a laminated glass beam altogether rather than the component individually. This eliminates the uncertainties of analytical approximations that are commonly adopted by most existing methods in which the composite shear/torsion stiffness is derived from its component mechanical properties. The photogrammetry technique increased the accuracy of the sectional rotation measurement by acquiring dense displacement sample points on the glass beam simultaneously. The accuracy of the photogrammetry setup and efficacy of the test design were proven by a micrometre and a monolithic glass beam test. One sample each for the polyvinyl butyral (PVB) and SentryGlas Plus (SGP) laminated glass beams were tested multiple times non-destructively to determine the ESSM. The result of the SGP laminated glass beam showed a closer agreement with the previous studies, however the result of the PVB laminated glass beam exhibited a larger difference from the previous studies. It also suggested that mechanical properties of the interlayer played an important role in the composite behaviour of the laminated glass beam. The experimental outcomes have demonstrated the proposed method is an accurate and effective technique for measuring the ESSM of laminated glass beams