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In order to perform a sensitivity analysis of Lagrangian trajectory models, Lagrangian trajectory simulations have been compared to six OpenMetBuoy-v2021 drifter trajectories in the Agulhas Current System (Jan-Mar 2023). Three different Lagrangian trajectory simulations have been assessed: (1) two offline Lagrangian tracking tools, OpenDrift and Parcels, (2) three Eulerian ocean surface current products, HYCOM, Mercator and Globcurrent, and (3) the addition of wind and/or wave forcing parameterizations. The latter has also been evaluated by strong ocean current, high wind speed and Stokes drift regimes. Firstly, using the same time stepping scheme and linear interpolation methods, the different Lagrangian simulators OpenDrift and Parcels, performed identically. Secondly, the Globcurrent product showed the highest mean skill of the three ocean current products, although it underestimated the speed for strong ocean currents due to its spatial resolution. The HYCOM and Mercator model simulations showed, respectively, 40\% and 15\% lower skill than the Globcurrent simulations. Finally, the addition of the Stokes drift and a wind drift factor (WDF), improved the Lagrangian simulation performance in skill and speed, especially in high wind (>10 m/s) and/or Stokes drift regimes (>0.15 m/s). The optimal WDF for the OpenMetBuoy-v2021 is found to be ~1.8\% and ~2.3\% for simulations including and excluding Stokes drift forcing respectively. To further improve the incorporation of Stokes drift and direct wind drag on the trajectory simulations, a more physically based solution is advised as there are still numerous wind and wave related processes that remain unresolved, like wave-current interactions and vertical shear. To statistically strengthen the conclusions from this research, incorporating additional observed drifter trajectories would be highly favourable.

We investigate the convergence of quasi-particle energies for periodic systems to the thermodynamic limit using increasingly large simulation cells corresponding to increasingly dense integration meshes in reciprocal space. The quasi-particle energies are computed at the level of equation-of-motion coupled-cluster theory for ionization (IP-EOM-CC) and electron attachment processes (EA-EOM-CC). By introducing an electronic correlation structure factor, the expected asymptotic convergence rates for systems with different dimensionality are formally derived. We rigorously test these derivations through numerical simulations for trans-Polyacetylene using IP/EA-EOM-CCSD and the G0W0@HF approximation, which confirm the predicted convergence behavior. Our findings provide a solid foundation for efficient schemes to correct finite-size errors in IP/EA-EOM-CCSD calculations., Comment: 16 pages, 9 figures

This study unveils the elusive presence of criminal signatures in cyberspace, validating for the first time their existence through statistical evidence. By applying the A priori algorithm to the modus operandi of Advanced Persistent Threats, extracted from an extensive corpus of over 17,000 articles spanning 2007 to 2020, we highlight the enduring patterns leveraged by sophisticated cyber criminals. Our findings verify the existence of unique signatures associated with advanced cybercriminals, bridging a crucial gap in current understanding of human behavior in cyber-attacks. This pivotal research sets the foundation for an entirely new academic intersection in cybersecurity and computational criminology., Comment: Communications The 7th Conference for Information & Communication Technologies for Organization & Society

We introduce a general framework for studying special subsets of rational points on an algebraic variety, termed $\mathcal{M}$-points. The notion of $\mathcal{M}$-points generalizes the concepts of integral points, Campana points and Darmon points. We introduce and study $M$-approximation over number fields and function fields, which is a notion that generalizes weak and strong approximation. We show that this property implies that the set of $\mathcal{M}$-points is not thin. We then give a simple characterisation of when a split toric variety satisfies $M$-approximation, generalizing work of Nakahara and Streeter. Further, we determine when the set of $\mathcal{M}$-points on a split toric variety is thin., Comment: 70 pages; Corollary 4.21 added, minor other changes

Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and self-assembled structures encoded in minima of an energy landscape. Here, we extend this paradigm to dynamic functionalities, such as motion and shape change, that are instead encoded in limit cycles or pathways of a dynamical system. We identify the two ingredients needed to learn time-dependent behaviors irrespective of experimental platforms: (i) learning rules with time delays and (ii) exposure to examples that break time-reversal symmetry during training. After providing a hands-on demonstration of these requirements using programmable LEGO toys, we turn to realistic particle-based simulations where the training rules are not programmed on a computer. Instead, we elucidate how they emerge from physico-chemical processes involving the causal propagation of fields, like in recent experiments on moving oil droplets with chemotactic signalling. Our trainable particles can self-assemble into structures that move or change shape on demand, either by retrieving the dynamic behavior previously seen during training, or by learning on the fly. This rich phenomenology is captured by a modified Hopfield spin model amenable to analytical treatment. The principles illustrated here provide a step towards von Neumann's dream of engineering synthetic living systems that adapt to the environment., Comment: 6 pages, 3 figures

Given its real-time capability to quantify mechanical tissue properties, ultrasound shear wave elastography holds significant promise in clinical musculoskeletal imaging. However, existing shear wave elastography methods fall short in enabling full-limb analysis of 3D anatomical structures under diverse loading conditions, and may introduce measurement bias due to sonographer-applied force on the transducer. These limitations pose numerous challenges, particularly for 3D computational biomechanical tissue modeling in areas like prosthetic socket design. In this feasibility study, a clinical linear ultrasound transducer system with integrated shear wave elastography capabilities was utilized to scan both a calibrated phantom and human limbs in a water tank imaging setup. By conducting 2D and 3D scans under varying compressive loads, this study demonstrates the feasibility of volumetric ultrasound shear wave elastography of human limbs. Our preliminary results showcase a potential method for evaluating 3D spatially varying tissue properties, offering future extensions to computational biomechanical modeling of tissue for various clinical scenarios., Comment: Ultrasonic Imaging. 2024

We present an active automata learning algorithm which learns a decomposition of a finite state machine, based on projecting onto individual outputs. This is dual to a recent compositional learning algorithm by Labbaf et al. (2023). When projecting the outputs to a smaller set, the model itself is reduced in size. By having several such projections, we do not lose any information and the full system can be reconstructed. Depending on the structure of the system this reduces the number of queries drastically, as shown by a preliminary evaluation of the algorithm., Comment: LearnAut 2024

Integrated superconducting spectrometers (ISSs) for wideband sub-mm astronomy utilise quasi-optical systems for coupling radiation from the telescope to the instrument. Misalignment in these systems is detrimental to the system performance. The common method of using an optical laser to align the quasi-optical components requires accurate alignment of the laser to the sub-mm beam coming from the instrument, which is not always guaranteed to a sufficient accuracy. We develop an alignment strategy for wideband ISSs directly utilising the sub-mm beam of the wideband ISS. The strategy should be applicable in both telescope and laboratory environments. Moreover, the strategy should deliver similar quality of the alignment across the spectral range of the wideband ISS. We measure misalignment in a quasi-optical system operating at sub-mm wavelengths using a novel phase and amplitude measurement scheme, capable of simultaneously measuring the complex beam patterns of a direct-detecting ISS across a harmonic range of frequencies. The direct detection nature of the MKID detectors in our device-under-test, DESHIMA 2.0, necessitates the use of this measurement scheme. Using geometrical optics, the measured misalignment, a mechanical hexapod, and an optimisation algorithm, we follow a numerical approach to optimise the positioning of corrective optics with respect to a given cost function. Laboratory measurements of the complex beam patterns are taken across a harmonic range between 205 and 391 GHz and simulated through a model of the ASTE telescope in order to assess the performance of the optimisation at the ASTE telescope. Laboratory measurements show that the optimised optical setup corrects for tilts and offsets of the sub-mm beam. Moreover, we find that the simulated telescope aperture efficiency is increased across the frequency range of the ISS after the optimisation., Comment: 10 pages, 12 figures. Accepted for publication by A&A

The objective of this study is to evaluate the mechanical properties and energy absorption characteristics of the gyroid, dual-lattice and spinodoid structures, as biomimetic lattices, through finite element analysis and experimental characterisation. As part of the study, gyroid and dual-lattice structures at 10 percent volume fraction were 3D-printed using an elastic resin, and mechanically tested under uniaxial compression. Computational models were calibrated to the observed experimental data and the response of higher volume fraction structures were simulated in an explicit finite element solver. Stress-strain data of groups of lattices at different volume fractions were studied and energy absorption parameters including total energy absorbed per unit volume, energy absorption efficiency and onset of densification strain were calculated. Also, the structures were characterized into bending-dominant and stretch-dominant structures, according to their nodal connectivity and Gibson-and-Ashby's law. The results of the study showed that the dual-lattice is capable of absorbing more energy at each volume fraction cohort. However, gyroid structures showed higher energy absorption efficiency and the onset of densification at higher strains. The spinodoid structure was found to be the poorest structure in terms of energy absorption, specifically at low volume fractions. Also, the results showed that the dual-lattice was a stretch dominated structure, while the gyroid structure was a bending dominated structure, which may be a reason that it is a better candidate for energy absorption applications.

Positive geometries provide a purely geometric point of departure for studying scattering amplitudes in quantum field theory. A positive geometry is a specific semi-algebraic set equipped with a unique rational top form - the canonical form. There are known examples where the canonical form of some positive geometry, defined in some kinematic space, encodes a scattering amplitude in some theory. Remarkably, the boundaries of the positive geometry are in bijection with the physical singularities of the scattering amplitude. The Amplituhedron, discovered by Arkani-Hamed and Trnka, is a prototypical positive geometry. It lives in momentum twistor space and describes tree-level (and the integrands of planar loop-level) scattering amplitudes in maximally supersymmetric Yang-Mills theory. In this dissertation, we study three positive geometries defined in on-shell momentum space: the Arkani-Hamed-Bai-He-Yan (ABHY) associahedron, the Momentum Amplituhedron, and the orthogonal Momentum Amplituhedron. Each describes tree-level scattering amplitudes for different theories in different spacetime dimensions. The three positive geometries share a series of interrelations in terms of their boundary posets and canonical forms. We review these relationships in detail, highlighting the author's contributions. We study their boundary posets, classifying all boundaries and hence all physical singularities at the tree level. We develop new combinatorial results to derive rank-generating functions which enumerate boundaries according to their dimension. These generating functions allow us to prove that the Euler characteristics of the three positive geometries are one. In addition, we discuss methods for manipulating canonical forms using ideas from computational algebraic geometry., Comment: PhD Dissertation

Field-Programmable Gate Array (FPGA)-based Software-Defined Radio (SDR) is well-suited for experimenting with advanced wireless communication systems, as it allows to alter the architecture promptly while obtaining high performance. However, programming the FPGA using a Hardware Description Language (HDL) is a time-consuming task for FPGA developers and difficult for software developers, which limits the potential of SDR. High-Level Synthesis (HLS) tools aid the designers by allowing them to program on a higher layer of abstraction. However, if not carefully designed, it may lead to a degradation in computing performance or significant increase in resource utilization. This work shows that it is feasible to design modern Orthogonal Frequency Division Multiplex (OFDM) baseband processing modules like channel estimation and equalization using HLS without sacrificing performance and to integrate them in an HDL design to form a fully-operational FPGA-based Wi-Fi (IEEE 802.11a/g/n) transceiver. Starting from no HLS experience, a design with minor overhead in terms of latency and resource utilization as compared to the HDL approach was created in less than one month. We show the readability of the sequential logic as coded in HLS, and discuss the lessons learned from the approach taken and the benefits it brings for further design and experimentation. The FPGA design generated by HLS was verified to be bit-true with its MATLAB implementation in simulation. Furthermore, we show its practical performance when deployed on a System-on-Chip (SoC)-based SDR using a professional wireless connectivity tester., Comment: 7 pages, extended version of poster accepted at FCCM 2023

The regeneration of the ruptured scapholunate interosseous ligament (SLIL) represents a clinical challenge. Here, we propose the use of a Bone-Ligament-Bone (BLB) 3D-printed polyethylene terephthalate (PET) scaffold for achieving mechanical stabilisation of the scaphoid and lunate following SLIL rupture. The BLB scaffold featured two bone compartments bridged by aligned fibres (ligament compartment) mimicking the architecture of the native tissue. The scaffold presented tensile stiffness in the range of 260+/-38 N/mm and ultimate load of 113+/-13 N, which would support physiological loading. A finite element analysis, using inverse finite element analysis for material property identification, showed an adequate fit between simulation and experimental data. The scaffold was then biofunctionalized using two different methods: injected with a Gelatin Methacryloyl solution containing human mesenchymal stem cell spheroids or seeded with tendon-derived stem cells and placed in a bioreactor to undergo cyclic deformation. The first approach demonstrated high cell viability, as cells migrated out of the spheroid and colonised the interstitial space of the scaffold. These cells adopted an elongated morphology suggesting the internal architecture of the scaffold exerted topographical guidance. The second method demonstrated the high resilience of the scaffold to cyclic deformation and the secretion of a fibroblastic related protein was enhanced by the mechanical stimulation. This process promoted the expression of relevant proteins, such as Tenomodulin, indicating mechanical stimulation may enhance cell differentiation and be useful prior to surgical implantation. In conclusion, the PET scaffold presented several promising characteristics for the immediate mechanical stabilisation of disassociated scaphoid and lunate and, in the longer-term, the regeneration of the ruptured SLIL.

In this study, we evaluate the performance of three algorithms as computational models of trabecular bone architecture, through systematic evaluation of morphometric, topological, and mechanical properties. Here, we consider the widely-used gyroid lattice structure, the recently-developed spinodoid structure and a structure similar to Voronoi lattices introduced here as the dual-lattice. While all computational models were calibrated to recreate the trabecular tissue volume (e.g., BV/TV), it was found that both the gyroid- and spinodoid-based structures showed substantial differences in many other morphometric and topological parameters and, in turn, showed lower effective mechanical properties compared to trabecular bone. The newly-developed dual-lattice structures better captured both morphometric parameters and mechanical properties, despite certain differences being evident their topological configuration compared to trabecular bone. Still, these computational algorithms provide useful platforms to investigate trabecular bone mechanics and for designing biomimetic structures, which could be produced through additive manufacturing for applications that include bone substitutes, scaffolds and porous implants. Furthermore, the software for the creation of the structures has been added to the open source toolbox GIBBON and is therefore freely available to the community., Comment: 30 pages, 8 figure, 3 tables Accepted on JMBBM

Finite element analysis (FEA) can be used to evaluate applied interface pressures and internal tissue strains for computational prosthetic socket design. This type of framework requires realistic patient-specific limb geometry and constitutive properties. In recent studies, indentations and inverse FEA with MRI-derived 3D patient geometries were used for constitutive parameter identification. However, long computational times and use of specialized equipment presents challenges for clinical deployment. In this study, we present a novel approach for constitutive parameter identification using a combination of FEA, ultrasound indentation, and shear wave elastography. Local shear modulus measurement using elastography during an ultrasound indentation experiment has particular significance for biomechanical modeling of the residual limb since there are known regional dependencies of soft tissue properties such as varying levels of scarring and atrophy. Beyond prosthesis design, this work has broader implications to the fields of muscle health and monitoring of disease progression.

In this paper we explore and expand the connection between two modern descriptions of scattering amplitudes, the CHY formalism and the framework of positive geometries, facilitated by the scattering equations. For theories in the CHY family whose $S$-matrix is captured by some positive geometry in the kinematic space, the corresponding canonical form can be obtained as the pushforward via the scattering equations of the canonical form of a positive geometry defined in the CHY moduli space. In order to compute these canonical forms in kinematic spaces, we study the general problem of pushing forward arbitrary rational differential forms via the scattering equations. We develop three methods which achieve this without ever needing to explicitly solve any scattering equations. Our results use techniques from computational algebraic geometry, including companion matrices and the global duality of residues, and they extend the application of similar results for rational functions to rational differential forms., Comment: 42 pages, 5 figures

DNA-coated colloids can crystallize into a multitude of lattices, ranging from face-centered cubic to diamond and thereby contribute to our understanding of crystallization and open avenues to producing structures with useful photonic properties. Despite the broad potential design space of DNA-coated colloids, the design cycle for synthesizing DNA-coated particles is slow: preparing a particle with a new type of DNA sequence takes more than one day and requires custom-made and chemically modified DNA that typically takes the supplier over a month to synthesize. Here, we introduce a method to generate particles with custom sequences from a single feed stock in under an hour at ambient conditions. Our method appends new DNA domains onto the DNA grafted to colloidal particles based on a template that takes the supplier less than a week to produce. The resultant particles crystallize as readily and at the same temperature as those produced via direct chemical synthesis. Moreover, we show that particles coated with a single sequence can be converted into a variety of building blocks with differing specificities by appending different DNA sequences to them. This approach to DNA-coated particle preparation will make it practical to identify optimal and complex particle sequence designs and to expand the use of DNA-coated colloids to a much broader range of investigators and commercial entities., Comment: manuscript 9 pages 6 figures. SI, 12 pages 6 figures

Software Defined Radio (SDR) platforms are valuable for research and development activities or high-end systems that demand real-time adaptable wireless protocols. While low latency can be achieved using the dedicated digital processing unit of a state-of-the-art SDR platform, its Radio Frequency (RF) front-end often poses a limitation in terms of turnaround time (TT), the time needed for switching from the receiving to the transmitting mode (or vice versa). Zero Intermediate Frequency (ZIF) transceivers are favorable for SDR, but suffer from self-interference even if the device is not currently transmitting. The strict MAC-layer requirements of Time Division Duplex (TDD) protocols like Wi-Fi cannot be achieved using configurable ZIF transceivers without having to compromise receiver sensitivity. Using a novel approach, we show that the TT using the AD9361 RF front-end can be as low as 640 ns, while the self-interference is at the same level as achieved by the conventional TDD mode, which has a TT of at least 55 {\mu}s. As compared to Frequency Division Duplex (FDD) mode, a decrease of receiver noise floor by about 13 dB in the 2.4 GHz band and by about 4.5 dB in the 5 GHz band is achieved., Comment: Accepted by IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks (WoWMoM 2022) as Work-In-Progress paper

Coupled cluster (CC) theory is often considered the gold standard of quantum-chemistry. For solids, however, the available software is scarce. We present CC-aims, which can interface ab initio codes with localized atomic orbitals and the CC for solids (CC4S) code by the group of A. Gr\"uneis. CC4S features a continuously growing selection of wave function-based methods including perturbation and CC theory. The CC-aims interface was developed for the FHI-aims code (https://fhi-aims.org) but is implemented such that other codes may use it as a starting point for corresponding interfaces. As CC4S offers treatment of both molecular and periodic systems, the CC-aims interface is a valuable tool, where DFT is either too inaccurate or too unreliable, in theoretical chemistry and materials science alike., Comment: Currently reviewed for publication in the JOSS journal (review process: https://github.com/openjournals/joss-reviews/issues/4040 ). The conciseness of the paper is due to the required word count of less than 1000 words by the journal (see https://joss.readthedocs.io/en/latest/submitting.html#what-should-my-paper-contain ). This manuscript is complete and introduces a new piece of software

In this paper we study the orthogonal momentum amplituhedron $\mathcal{O}_k$, a recently introduced positive geometry that encodes the tree-level scattering amplitudes in ABJM theory. We generate the full boundary stratification of $\mathcal{O}_k$ and show that its boundaries can be labelled by so-called orthogonal Grassmannian forests (OG forests). We also determine the generating function for enumerating boundaries according to their dimension and show that the Euler characteristic of $\mathcal{O}_k$ equals one. This provides a strong indication that the orthogonal momentum amplituhedron is homeomorphic to a ball. This paper is supplemented with the Mathematica package "orthitroids" which contains useful functions for studying the positive orthogonal Grassmannian and the orthogonal momentum amplituhedron., Comment: 19 pages, 7 figures

The Exponential Formula allows one to enumerate any class of combinatorial objects built by choosing a set of connected components and placing a structure on each connected component which depends only on its size. There are multiple variants of this result, including Speicher's result for noncrossing partitions, as well as analogues of the Exponential Formula for series-reduced planar trees and forests. In this paper we use these formulae to give generating functions contracted Grassmannian trees and forests, certain graphs whose vertices are decorated with a helicity. Along the way we enumerate bipartite planar trees and forests, and we apply our results to enumerate various families of permutations: for example, bipartite planar trees are in bijection with separable permutations. Our generating function for Grassmannian forests can be interpreted as the rank generating function for the boundary strata of the momentum amplituhedron, an object which encodes the tree-level S-matrix of maximally supersymmetric Yang-Mills theory. This allows us to verify that the Euler characteristic of the momentum amplituhedron is 1., Comment: 25 pages, multiple figures, comments welcome

Randomization is a powerful technique to create robust controllers, in particular in partially observable settings. The degrees of randomization have a significant impact on the system performance, yet they are intricate to get right. The use of synthesis algorithms for parametric Markov chains (pMCs) is a promising direction to support the design process of such controllers. This paper shows how to define and evaluate gradients of pMCs. Furthermore, it investigates varieties of gradient descent techniques from the machine learning community to synthesize the probabilities in a pMC. The resulting method scales to significantly larger pMCs than before and empirically outperforms the state-of-the-art, often by at least one order of magnitude., Comment: Technical Report VMCAI22 submission

We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms up to 2.5 order, and the first order Taylor expansion to the Einstein-Infeld-Hoffmann equations of motion. The degree to which our system is relativistic depends on the scaling of the total mass (the unit size was 1 parsec). Using the Brutus method of convergence, we test for time-reversibility in the conservative regime, and demonstrate that we are able to obtain definitive solutions to the relativistic three-body problem. It is also confirmed that the minimal required numerical accuracy for a successful time-reversibility test correlates with the amplification factor of an initial perturbation. When we take into account dissipative effects through gravitational wave emission, we find that the duration of the resonance, and the amount of exponential growth of small perturbations depend on the mass scaling. For a unit mass <= 10 MSun, the system behavior is indistinguishable from the Newtonian case, and the resonance always ends in a binary and one escaping body. For a mass scaling up to 1e7 MSun, relativity gradually becomes more prominent, but the majority of the systems still dissolve. The first mergers start to appear for a mass of ~1e5 MSun, and between 1e7 MSun and 1e9 MSun all systems end prematurely in a merger. These mergers are preceded by a gravitational wave driven in-spiral. For a mass scaling >= 1e9 MSun, all systems result in a gravitational wave merger upon the first close encounter. Relativistic three-body encounters thus provide an efficient pathway for resolving the final parsec problem. The onset of mergers at the characteristic mass scale of 1e7 MSun potentially leaves an imprint in the mass function of supermassive black holes., Comment: Accepted by Phys Rev D. 10 pages, 6 figures

Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes. In this note we consider tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills theory and present a Grassmannian formulation of their celestial counterparts. This result paves the way towards a geometric picture for celestial superamplitudes, in the spirit of positive geometries., Comment: 11 pages

CSI (Channel State Information) of WiFi systems contains the environment channel response between the transmitter and the receiver, so the people/objects and their movement in between can be sensed. To get CSI, the receiver performs channel estimation based on the pre-known training field of the transmitted WiFi signal. CSI related technology is useful in many cases, but it also brings concerns on privacy and security. In this paper, we open sourced a CSI fuzzer to enhance the privacy and security of WiFi CSI applications. It is built and embedded into the transmitter of openwifi, which is an open source full-stack WiFi chip design, to prevent unauthorized sensing without sacrificing the WiFi link performance. The CSI fuzzer imposes an artificial channel response to the signal before it is transmitted, so the CSI seen by the receiver will indicate the actual channel response combined with the artificial response. Only the authorized receiver, that knows the artificial response, can calculate the actual channel response and perform the CSI sensing. Another potential application of the CSI fuzzer is covert channels based on a set of pre-defined artificial response patterns. Our work resolves the pain point of implementing the anti-sensing idea based on the commercial off-the-shelf WiFi devices., Comment: Accepted by ACM WiSec 2021

For biologically relevant macromolecules such as intrinsically disordered proteins, internal degrees of freedom that allow for shape changes have a large influence on both the motion and function of the compound. A detailed understanding of the effect of flexibility is needed in order to explain their behavior. Here, we study a model system of freely-jointed chains of three to six colloidal spheres, using both simulations and experiments. We find that in spite of their short lengths, their conformational statistics are well described by two-dimensional Flory theory, while their average translational and rotational diffusivity follow the Kirkwood-Riseman scaling. Their maximum flexibility does not depend on the length of the chain, but is determined by the near-wall in-plane translational diffusion coefficient of an individual sphere. Furthermore, we uncover shape-dependent effects in the short-time diffusivity of colloidal tetramer chains, as well as non-zero couplings between the different diffusive modes. Our findings may have implications for understanding both the diffusive behavior and the most likely conformations of macromolecular systems in biology and industry, such as proteins, polymers, single-stranded DNA and other chain-like molecules., Comment: 19 pages, 10 figures

We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata for infinite alphabets. The algorithm runs in exponential time, and in polynomial time for a fixed number of registers. As a special case, we can decide, with the same complexity, language equivalence for unambiguous register automata, which improves previous results in three ways: (a) we allow for order comparisons on atoms, and not just equality; (b) the complexity is exponentially better; and (c) we allow automata with guessing., Comment: Journal Version for TheoretiCS

In recent years, it has been understood that color-ordered scattering amplitudes can be encoded as logarithmic differential forms on positive geometries. In particular, amplitudes in maximally supersymmetric Yang-Mills theory in spinor helicity space are governed by the momentum amplituhedron. Due to the group-theoretic structure underlying color decompositions, color-ordered amplitudes enjoy various identities which relate different orderings. In this paper, we show how the Kleiss-Kuijf relations arise from the geometry of the momentum amplituhedron. We also show how similar relations can be realised for the kinematic associahedron, which is the positive geometry of bi-adjoint scalar cubic theory., Comment: 44 pages, 19 figures

Code that is highly optimized poses a problem for program-level verification: programmers can employ various clever tricks that are non-trivial to reason about. For cryptography on low-power devices, it is nonetheless crucial that implementations be functionally correct, secure, and efficient. These are usually crafted in hand-optimized machine code that eschew conventional control flow as much as possible. We have formally verified such code: a library which implements elliptic curve cryptography on 8-bit AVR microcontrollers. The chosen implementation is the most efficient currently known for this microarchitecture. It consists of over 3000 lines of assembly instructions. Building on earlier work, we use the Why3 platform to model the code and prove verification conditions, using automated provers. We expect the approach to be re-usable and adaptable, and it allows for validation. Furthermore, an error in the original implementation was found and corrected, at the same time reducing its memory footprint. This shows that practical verification of cutting-edge code is not only possible, but can in fact add to its efficiency -- and is clearly necessary., Comment: 19 pages, 5 figures. accepted at NFM 2021 (without appendix)