The Reidemeister spectrum of 2-step nilpotent groups determined by graphs

In this paper we study the Reidemeister spectrum of 2-step nilpotent groups associated to graphs. We develop three methods, based on the structure of the graph, that can be used to determine the Reidemeister spectrum of the associated group in terms of the Reidemeister spectra of groups associated to smaller graphs. We illustrate our methods for several families of graphs, including all the groups associated to a graph with at most four vertices. We also apply our results in the context of topological fixed point theory for nilmanifolds

R∞R_{\infty}-property for groups commensurable to nilpotent quotients of RAAGs

Let $G$ be a group and $\varphi$ an automorphism of $G$. Two elements $x,y \in G$ are said to be $\varphi$-conjugate if there exists a third element $z \in G$ such that $z x \varphi(z)^{-1} = y$. Being $\varphi$-conjugate defines an equivalence relation on $G$. The group $G$ is said to have the $R_{\infty}$-property if all its automorphisms $\varphi$ have infinitely many $\varphi$-conjugacy classes. For finitely generated torsion-free nilpotent groups, the so-called Mal'cev completion of the group is a useful tool in studying this property. Two groups have isomorphic Mal'cev completions if and only if they are abstractly commensurable. This raises the question whether the $R_{\infty}$-property is invariant under abstract commensurability within the class of finitely generated torsion-free nilpotent groups. We show that the answer to this question is negative and provide counterexamples within a class of 2-step nilpotent groups associated to edge-weighted graphs. These groups are commensurable to 2-step nilpotent quotients of right-angled Artin groups.Comment: 25 page

Verifying Sanitizer Correctness through Black-Box Learning:A Symbolic Finite Transducer Approach

String sanitizers are widely used functions for preventing injection attacks such as SQL injections and cross-site scripting (XSS). It is therefore crucial that the implementations of such string sanitizers are correct. We present a novel approach to reason about a sanitizer’s correctness by automatically generating a model of the implementation and comparing it to a model of the expected behaviour. To automatically derive a model of the implementation of the sanitizer, this paper introduces a black-box learning algorithm that derives a Symbolic Finite Transducer (SFT). This black-box algorithm uses membership and equivalence oracles to derive such a model. In contrast to earlier research, SFTs not only describe the input or output language of a sanitizer but also how a sanitizer transforms the input into the output. As a result, we can reason about the transformations from input into output that are performed by the sanitizer. We have implemented this algorithm in an open-source tool of which we show that it can reason about the correctness of non-trivial sanitizers within a coupleof minutes without any adjustments to the existing sanitizers

Two-dimensional oxygen-diffusion modelling for FLASH proton therapy with pencil beam scanning—Impact of diffusive tissue properties, dose, dose rate and scan patterns

Objective:Oxygen depletion is generally believed to play an important role in the FLASH effect—a differential reduction of the radiosensitivity of healthy tissues, relative to that of the tumour under ultra-high dose-rate (UHDR) irradiation conditions. In proton therapy (PT) with pencil-beam scanning (PBS), the deposition of dose, and, hence, the degree of (radiolytic) oxygen depletion varies both spatially and temporally. Therefore, the resulting oxygen concentration and the healthy-tissue sparing effect through radiation-induced hypoxia varies both spatially and temporally as well. Approach. We propose and numerically solve a physical oxygen diffusion model to study these effects and their dependence on tissue parameters and the scan pattern in pencil-beam delivery. Since current clinical FLASH PT (FLASH-PT) is based on 250 MeV shoot-through (transmission) beams, for which dose and dose rate (DR) hardly vary with depth compared to the variation transverse to the beam axis, we focus on the two-dimensional case. We numerically integrate the model to obtain the oxygen concentration in each voxel as a function of time and extract voxel-based and spatially and temporarily integrated metrics for oxygen (FLASH) enhanced dose. Furthermore, we evaluate the impact on oxygen enhancement of standard pencil-beam delivery patterns and patterns that were optimised on dose-rate. Our model can contribute to the identification of tissue properties and pencil-beam delivery parameters that are critical for FLASH-PT and it may be used for the optimisation of FLASH-PT treatment plans and their delivery. Main results:(i) the diffusive properties of oxygen are critical for the steady state concentration and therefore the FLASH effect, even more so in two dimensions when compared to one dimension. (ii) The FLASH effect through oxygen depletion depends primarily on dose and less on other parameters. (iii) At a fixed fraction dose there is a slight dependence on DR. (iv) Scan patterns optimised on DR slightly increase the oxygen induced FLASH effect.Significance: To our best knowledge, this is the first study assessing the impact of scan-pattern optimization (SPO) in FLASH-PT with PBS on a biological FLASH model. While the observed impact of SPO is relatively small, a larger effect is expected for larger target volumes. A better understanding of the FLASH effect and the role of oxygen (depletion) therein is essential for the further development of FLASH-PT with PBS, and SPO.</p

Finite element modeling of a rubber V-belt CVT describing pulley clearance : traineeship report

No abstract

Verifying Sanitizer Correctness through Black-Box Learning: A Symbolic Finite Transducer Approach

String sanitizers are widely used functions for preventing injection attacks such as SQL injections and cross-site scripting (XSS). It is therefore crucial that the implementations of such string sanitizers are correct. We present a novel approach to reason about a sanitizer’s correctness by automatically generating a model of the implementation and comparing it to a model of the expected behaviour. To automatically derive a model of the implementation of the sanitizer, this paper introduces a black-box learning algorithm that derives a Symbolic Finite Transducer (SFT). This black-box algorithm uses membership and equivalence oracles to derive such a model. In contrast to earlier research, SFTs not only describe the input or output language of a sanitizer but also how a sanitizer transforms the input into the output. As a result, we can reason about the transformations from input into output that are performed by the sanitizer. We have implemented this algorithm in an open-source tool of which we show that it can reason about the correctness of non-trivial sanitizers within a couple of minutes without any adjustments to the existing sanitizers

Human-Prosthetic Interaction (HumanIT): A study protocol for a clinical trial evaluating brain neuroplasticity and functional performance after lower limb loss.

BackgroundLower limb amputation contributes to structural and functional brain alterations, adversely affecting gait, balance, and overall quality of life. Therefore, selecting an appropriate prosthetic ankle is critical in enhancing the well-being of these individuals. Despite the availability of various prostheses, their impact on brain neuroplasticity remains poorly understood.ObjectivesThe primary objective is to examine differences in the degree of brain neuroplasticity using magnetic resonance imaging (MRI) between individuals wearing a new passive ankle prosthesis with an articulated ankle joint and a standard passive prosthesis, and to examine changes in brain neuroplasticity within these two prosthetic groups. The second objective is to investigate the influence of prosthetic type on walking performance and quality of life. The final objective is to determine whether the type of prosthesis induces differences in the walking movement pattern.MethodsParticipants with a unilateral transtibial amputation will follow a 24-week protocol. Prior to rehabilitation, baseline MRI scans will be performed, followed by allocation to the intervention arms and commencement of rehabilitation. After 12 weeks, baseline functional performance tests and a quality of life questionnaire will be administered. At the end of the 24-week period, participants will undergo the same MRI scans, functional performance tests and questionnaire to evaluate any changes. A control group of able-bodied individuals will be included for comparative analysis.ConclusionThis study aims to unravel the differences in brain neuroplasticity and prosthesis type in patients with a unilateral transtibial amputation and provide insights into the therapeutic benefits of prosthetic devices. The findings could validate the therapeutic benefits of more advanced lower limb prostheses, potentially leading to a societal impact ultimately improving the quality of life for individuals with lower limb amputation.Trial registrationNCT05818410 (Clinicaltrials.gov)