On the maximum number of subgroups of a finite group

Given a finite group $R$, we let $\mathrm{Sub}(R)$ denote the collection of all subgroups of $R$. We show that $|\mathrm{Sub}(R)|< c\cdot |R|^{\frac{\log_2|R|}{4}}$, where $c<7.372$ is an explicit absolute constant. This result is asymptotically best possible. Indeed, as $|R|$ tends to infinity and $R$ is an elementary abelian $2$-group, the ratio $$\frac{|\mathrm{Sub}(R)|}{|R|^{\frac{\log_2|R|}{4}}}$$ tends to $c$.Comment: 22 page

Slip flow in elliptic microducts with constant heat flux

This paper outlines a numerical model for determining the dynamic and thermal performances of a rarefied fluid flowing in a microduct with elliptical cross-section. A slip flow is considered, in laminar steady state condition, in fully developed forced convection, with Knudsen number in the range 0.001-0.1, in H1 boundary conditions. The velocity and temperature distributions are determined in the elliptic cross-section, for different values of both aspect ratio γ and Knudsen number, resorting to the Comsol Multiphysics software, to solve the momentum and energy equations. The friction factors (or Poiseuille numbers) and the convective heat transfer coefficients (or Nusselt numbers) are calculated and presented in graphs and tables. The numerical solution is validated resorting to data available in literature for continuum flow in elliptic cross-sections (Kn = 0) and for slip flow in circular ducts (γ = 1). A further benchmark is carried out for the velocity profile for slip flow in elliptical cross-sections, thanks to a recent analytical solution obtained using elliptic cylinder coordinates and the separation of variables method. The Poiseuille and Nusselt numbers for elliptic cross-sections are discussed. The results may be used to predict pressure drop and heat transfer performance in metallic microducts with elliptic cross-section, produced by microfabrication for microelectromechanical systems (MEMS)

On the proportion of derangements and on suborbits in finite transitive groups

We find a lower bound on the proportion of derangements in a finite transitive group that depends on the minimal nontrivial subdegree. As a consequence, we prove that, if $\Gamma$ is a $G$-vertex-transitive digraph of valency $d\ge 1$, then the proportion of derangements in $G$ is greater than $1/2d$.Comment: 7 page

Influence of Outdoor Air Conditions on the Air Source Heat Pumps Performance

Abstract The purpose of the present work is the investigation of the effect of the outdoor air temperature and relative humidity on the performance of an air heat pump, when the reverse-cycle defrosting is considered. The frost formation process has been analyzed by developing a simplified model which relates the number of defrost cycles to the outdoor air conditions. Moreover the energy consumption due to the defrosting has been taken into account in the evaluation of the heat pump performance. The results, carried out for many Italian sites, point out that the outdoor air conditions play an important role in determining the amount of defrost cycles; however the frost formation is mainly affected by the relative humidity. The analysis highlights also that the defrosting contribution on the heat pump performance is not negligible when the heat pump that operates in wet weather, although cold; in these conditions the hourly COP may be reduced by up to 20%. However, this effect becomes less relevant, but not negligible, when the seasonal heat pump performance is evaluated; the maximum decrease of SCOP, observed for the all analyzed cases, is less than 13%

Analog Memristive Synapse in Spiking Networks Implementing Unsupervised Learning

Emerging brain-inspired architectures call for devices that can emulate the functionality of biological synapses in order to implement new efficient computational schemes able to solve ill-posed problems. Various devices and solutions are still under investigation and, in this respect, a challenge is opened to the researchers in the field. Indeed, the optimal candidate is a device able to reproduce the complete functionality of a synapse, i.e. the typical synaptic process underlying learning in biological systems (activity-dependent synaptic plasticity). This implies a device able to change its resistance (synaptic strength, or weight) upon proper electrical stimuli (synaptic activity) and showing several stable resistive states throughout its dynamic range (analog behavior). Moreover, it should be able to perform spike timing dependent plasticity (STDP), an associative homosynaptic plasticity learning rule based on the delay time between the two firing neurons the synapse is connected to. This rule is a fundamental learning protocol in state-of-art networks, because it allows unsupervised learning. Notwithstanding this fact, STDP-based unsupervised learning has been proposed several times mainly for binary synapses rather than multilevel synapses composed of many binary memristors. This paper proposes an HfO2-based analog memristor as a synaptic element which performs STDP within a small spiking neuromorphic network operating unsupervised learning for character recognition. The trained network is able to recognize five characters even in case incomplete or noisy characters are displayed and it is robust to a device-to-device variability of up to +/-30%

KEMTUB012-NI2, a novel potent tubulysin analog that selectively targets hypoxic cancer cells and is potentiated by cytochrome p450 reductase downregulation

Peer reviewedPublisher PD

FluTAS: A GPU-accelerated finite difference code for multiphase flows

We present the Fluid Transport Accelerated Solver, FluTAS, a scalable GPU code for multiphase flows with thermal effects. The code solves the incompressible Navier-Stokes equation for two-fluid systems, with a direct FFT-based Poisson solver for the pressure equation. The interface between the two fluids is represented with the Volume of Fluid (VoF) method, which is mass conserving and well suited for complex flows thanks to its capacity of handling topological changes. The energy equation is explicitly solved and coupled with the momentum equation through the Boussinesq approximation. The code is conceived in a modular fashion so that different numerical methods can be used independently, the existing routines can be modified, and new ones can be included in a straightforward and sustainable manner. FluTAS is written in modern Fortran and parallelized using hybrid MPI/OpenMP in the CPU-only version and accelerated with OpenACC directives in the GPU implementation. We present different benchmarks to validate the code, and two large-scale simulations of fundamental interest in turbulent multiphase flows: isothermal emulsions in HIT and two-layer Rayleigh-B\'enard convection. FluTAS is distributed through a MIT license and arises from a collaborative effort of several scientists, aiming to become a flexible tool to study complex multiphase flows

Physical Implementation of a Tunable Memristor-based Chua's Circuit

Nonlinearity is a central feature in demanding computing applications that aim to deal with tasks such as optimization or classification. Furthermore, the consensus is that nonlinearity should not be only exploited at the algorithm level, but also at the physical level by finding devices that incorporate desired nonlinear features to physically implement energy, area and/or time efficient computing applications. Chaotic oscillators are one type of system powered by nonlinearity, which can be used for computing purposes. In this work we present a physical implementation of a tunable Chua's circuit in which the nonlinear part is based on a nonvolatile memristive device. Device characterization and circuit analysis serve as guidelines to design the circuit and results prove the possibility to tune the circuit oscillatory response by electrically programming the device.Comment: Accepted by IEEE 48th European Solid State Circuits Conference (ESSCIRC 2022

Chua's Circuit With Tunable Nonlinearity Based on a Nonvolatile Memristor: Design and Realization

Nonvolatile memristive devices display nonlinear characteristics suitable for implementing circuits exhibiting oscillations or more complex dynamic behaviors, including chaos. However, the results presented in related works are mostly limited to simulations and employing ideal memristor models whose resistance is governed by a charge-flux relation that is not connected to real devices, thus hindering the realization of such nonlinear oscillators. In this work, we present the framework for the physical implementation of a tunable memristor Chua's circuit, which is based on a nonvolatile memristive device that provides the nonlinear conductance required by the circuit and the possibility to tune it for the purpose of selecting among different oscillation patterns. We first establish design guidelines to guarantee complex oscillations in the tunable memristor Chua's circuit. Further, we physically implement the circuit after characterizing and modeling the tunable current-voltage characteristic of a real device. Our circuit successfully generates different oscillation patterns just by programming the nonvolatile memristive device to different states. The devised design guidelines and device modeling were used to extend the experimental work and draw further requirements for device properties for a successful circuit implementation