Existence and Stability of Periodic Orbits of Periodic Difference Equations with Delays

In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xn = ƒ(n−1, xn−k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p/gcd(p,k) - periodic difference equations. We give formulas for calculating the number of different periodic orbits under certain conditions. In addition, when p and k are relatively prime integers, we introduce what we call the pk-Sharkovsky’s ordering of the positive integers, and extend Sharkovsky’s theorem to periodic difference equations with delays. Finally, we characterize global stability and show that the period of a globally asymptotically stable orbit must divide p

An Extension of Sharkovsky’s Theorem to Periodic Difference Equations

We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties

An integrated circuit for chip-based analysis of enzyme kinetics and metabolite quantification

We have created a novel chip-based diagnostic tools based upon quantification of metabolites using enzymes specific for their chemical conversion. Using this device we show for the first time that a solid-state circuit can be used to measure enzyme kinetics and calculate the Michaelis-Menten constant. Substrate concentration dependency of enzyme reaction rates is central to this aim. Ion-sensitive field effect transistors (ISFET) are excellent transducers for biosensing applications that are reliant upon enzyme assays, especially since they can be fabricated using mainstream microelectronics technology to ensure low unit cost, mass-manufacture, scaling to make many sensors and straightforward miniaturisation for use in point-of-care devices. Here, we describe an integrated ISFET array comprising 216 sensors. The device was fabricated with a complementary metal oxide semiconductor (CMOS) process. Unlike traditional CMOS ISFET sensors that use the Si3N4 passivation of the foundry for ion detection, the device reported here was processed with a layer of Ta2O5 that increased the detection sensitivity to 45 mV/pH unit at the sensor readout. The drift was reduced to 0.8 mV/hour with a linear pH response between pH 2 – 12. A high-speed instrumentation system capable of acquiring nearly 500 fps was developed to stream out the data. The device was then used to measure glucose concentration through the activity of hexokinase in the range of 0.05 mM – 231 mM, encompassing glucose’s physiological range in blood. Localised and temporal enzyme kinetics of hexokinase was studied in detail. These results present a roadmap towards a viable personal metabolome machine

Multi-level network resilience: traffic analysis, anomaly detection and simulation

Traffic analysis and anomaly detection have been extensively used to characterize network utilization as well as to identify abnormal network traffic such as malicious attacks. However, so far, techniques for traffic analysis and anomaly detection have been carried out independently, relying on mechanisms and algorithms either in edge or in core networks alone. In this paper we propose the notion of multi-level network resilience, in order to provide a more buy pill robust traffic analysis and anomaly detection architecture, combining mechanisms and algorithms operating in a coordinated fashion both in the edge and in the core networks. This work is motivated by the potential complementarities between the research being developed at IIT Madras and Lancaster University. In this paper we describe the current work being developed at IIT Madras and Lancaster on traffic analysis and anomaly detection, and outline the principles of a multi-level resilience architecture

Radiative D∗D^* Decay Using Heavy Quark and Chiral Symmetry

The implications of chiral $SU(3)_L \times SU(3)_R$ symmetry and heavy quark symmetry for the radiative decays $D^{*0}\to D^0\gamma$, $D^{*+}\to D^+\gamma$, and $D_s^*\to D_s\gamma$ are discussed. Particular attention is paid to $SU(3)$ violating contributions of order $m_q^{1/2}$. Experimental data on these radiative decays provide constraints on the $D^* D\pi$ coupling.Comment: 9 pages plus 3 pages of figures in POSTSCRIPT file appended to TeX file (uses harvmac.tex and tables.tex), UCSD/PTH 92-31, CALT-68-1816, EFI-92-45, CERN-TH.6650/9

SuNeRF: Validation of a 3D Global Reconstruction of the Solar Corona Using Simulated EUV Images

Extreme Ultraviolet (EUV) light emitted by the Sun impacts satellite operations and communications and affects the habitability of planets. Currently, EUV-observing instruments are constrained to viewing the Sun from its equator (i.e., ecliptic), limiting our ability to forecast EUV emission for other viewpoints (e.g. solar poles), and to generalize our knowledge of the Sun-Earth system to other host stars. In this work, we adapt Neural Radiance Fields (NeRFs) to the physical properties of the Sun and demonstrate that non-ecliptic viewpoints could be reconstructed from observations limited to the solar ecliptic. To validate our approach, we train on simulations of solar EUV emission that provide a ground truth for all viewpoints. Our model accurately reconstructs the simulated 3D structure of the Sun, achieving a peak signal-to-noise ratio of 43.3 dB and a mean absolute relative error of 0.3\% for non-ecliptic viewpoints. Our method provides a consistent 3D reconstruction of the Sun from a limited number of viewpoints, thus highlighting the potential to create a virtual instrument for satellite observations of the Sun. Its extension to real observations will provide the missing link to compare the Sun to other stars and to improve space-weather forecasting.Comment: Accepted at Machine Learning and the Physical Sciences workshop, NeurIPS 202

Understanding the interaction of organic corrosion inhibitors with copper at the molecular scale : benzotriazole on Cu(110)

M.T. gratefully acknowledges financial support from Lubrizol Limited and, together with J.E., thank the Engineering and Physical Sciences Research Council (EPSRC) grant EP/L015307/1 for the Molecular Analytical Science Centre for Doctoral Training (MAS-CDT). C.G acknowledges the Euler cluster managed by the HPC team at ETH Zurich for computational resources and is grateful for computational support from the UK national high performance computing service, ARCHER, for which access was obtained via the UKCP consortium and funded by EPSRC grant EP/P022561/1.Benzotriazole (BTAH) has been used for several industrial applications, but most commonly as a corrosion inhibitor for copper, since the 1950s. However, the mechanism of its interaction with copper surfaces at the atomistic scale is still a matter of debate. Here, the adsorption of BTAH onto a clean Cu(110) surface has been investigated by a combination of scanning tunnelling microscopy, X-ray photoelectron spectroscopy, high resolution electron energy loss spectroscopy and density functional theory calculations. Different supramolecular structures have been observed depending on molecular coverage and annealing. In the low coverage regime, flat lying deprotonated species are formed which give way to benzotriazolate molecules in an upright configuration by increasing the BTAH exposure. The ensuing monolayer is self-limiting but, upon annealing above 150 °C, transforms into a highly ordered nano-ridge structure resulting from a significant in-plane and out-of-plane reconstruction of the surface. All structures are characterised by a strong molecule-substrate interaction and the high coverage phases are dominated by the formation of metal-organic complexes between copper adatoms and benzotriazolate species. These findings shed light on the nature and strength of the interaction occurring between BTAH and copper which lies at the basis of the effectiveness of this prototypical corrosion inhibitor.PostprintPeer reviewe

A Fractionated Space Weather Base at L_5 using CubeSats and Solar Sails

The Sun–Earth L_5 Lagrange point is an ideal location for an operational space weather forecasting mission to provide early warning of Earth-directed solar storms (coronal mass ejections, shocks and associated solar energetic particles). Such storms can cause damage to power grids, spacecraft, communications systems and astronauts, but these effects can be mitigated if early warning is received. Space weather missions at L5 have been proposed using conventional spacecraft and chemical propulsion at costs of hundreds of millions of dollars. Here we describe a mission concept that could accomplish many of the goals at a much lower cost by dividing the payload among a cluster of interplanetary CubeSats that reach orbits around L5 using solar sails