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Let $S$ be a (compact)\ Riemann surface of genus greater than one. Two automorphism of $S$ are topologically equivalent if they are conjugated by a homeomorphism. The topological classification of automorphisms is a classical problem and its study was initiated by J. Nielsen who in the thirties classified conformal ones. The case of anticonformal automorphisms is more involved and was solved by K. Yocoyama in the 80s-90s. In order to decide whether two anti-conformal automorphisms are equivalent, it is usually necessary to take into account many invariants, some of which are difficult to compute. In this work we present some situations where the topological equivalence is mainly due to the genus of some quotient surfaces and the algebraic structure of the automorphism group. An anticonformal square root of a conformal automorphism $f$ is an anticonformal automorphism $g$ such that $g^{2}=f$ . Let $g_{1}$ and $g_{2}$ be anticonformal square roots of the same conformal automorphism of order $m$, where $m$ is an even integer. If genus of $S/\left\langle g_{1},g_{2} \right\rangle $ is even and genus of $S/\left\langle g_{i}\right\rangle $ is $\neq2$ we prove that $\left\langle g_{1}\right\rangle $ and $\left\langle g_{2}\right\rangle $ are topologically equivalent. If genus of $S/\left\langle g_{1},g_{2}\right\rangle $ is odd and $\left\langle g_{1},g_{2}\right\rangle $ is abelian we obtain that $\left\langle g_{1}\right\rangle $ and $\left\langle g_{2}\right\rangle $ are topologically equivalent. We give examples to justify the condition genus of $S/\left\langle g_{i}\right\rangle $ $\neq2$ and $\left\langle g_{1},g_{2}\right\rangle $ abelian in each case.

Animals chain movements into long-lived motor strategies, exhibiting variability across scales that reflects the interplay between internal states and environmental cues. To reveal structure in such variability, we build Markov models of movement sequences that bridges across time scales and enables a quantitative comparison of behavioral phenotypes among individuals. Applied to larval zebrafish responding to diverse sensory cues, we uncover a hierarchy of long-lived motor strategies, dominated by changes in orientation distinguishing cruising versus wandering strategies. Environmental cues induce preferences along these modes at the population level: while fish cruise in the light, they wander in response to aversive stimuli, or in search for appetitive prey. As our method encodes the behavioral dynamics of each individual fish in the transitions among coarse-grained motor strategies, we use it to uncover a hierarchical structure in the phenotypic variability that reflects exploration-exploitation trade-offs. Across a wide range of sensory cues, a major source of variation among fish is driven by prior and/or immediate exposure to prey that induces exploitation phenotypes. A large degree of variability that is not explained by environmental cues unravels motivational states that override the sensory context to induce contrasting exploration-exploitation phenotypes. Altogether, by extracting the timescales of motor strategies deployed during navigation, our approach exposes structure among individuals and reveals internal states tuned by prior experience., Comment: 31 pages, 7 main figures, 1 supplementary table and 8 supplementary figures

CrI3 is a layered ferromagnetic insulator that has recently attracted enormous interest as it was the first example of a stand-alone monolayer ferromagnet, paving the way towards the study of two-dimensional magnetic materials and their use as building blocks of hybrid van der Waals layered heterostructures. Here we go one step down in the dimensionality ladder and report the synthesis and characterization of a tubular one-dimensional van der Waals heterostructure where CrI3 nanotubes are encapsulated within multiwall carbon nanotubes, integrating a magnetic insulator and a conductor. By means of the capillary filling of multi-wall carbon nanotubes (MWCNT), we obtained single-wall CrI3 nanotubes with diameters ranging between 2 nm and 10 nm, with an average of 5.3 nm. Using aberration corrected electron microscopy in combination with spectroscopic techniques we confirm the structure and chemical composition of the nanotubes. SQUID measurements, combined with element-specific X-ray magnetic circular dichroism (XMCD) indicate unequivocally that the Cr atoms in encapsulated CrI3 nanotubes are magnetic with a collective state compatible with a radial magnetization state predicted both by first-principles calculations and a model Hamiltonian. Our results represent a step forward in establishing 1D van der Waals heterostructures as a playground for the exploration of non-collinear magnetic states arising from the interplay between magnetic anisotropy and curvature in tubular geometries., Comment: 19 pages with 5 figures

Animal locomotion is often subject to constraints arising from anatomical/physiological asymmetries. We use the nematode C.~elegans as a minimal model system to ask whether such constraints might shape locomotion patterns optimized during evolution. We focus on turning behaviours in two contrasting environmental contexts: (i) random exploration in the absence of strong stimuli and (ii) acute avoidance (escape) navigation upon encountering a strong aversive stimulus. We characterise the full repertoire of reorientation behaviours, including gradual reorientations and various posturally distinct sharp turns. During exploration, our measurements and theoretical modelling indicate that orientation fluctuations on short timescales are, on average, optimized to compensate the constraining gradual turn bias on long timescales. During escape, our data suggests that the reorientation is controlled not by an analog logic of continuous turn-amplitude modulations, but rather through the digital logic of selecting discrete turn types, leading to a symmetric escape performance despite strongly asymmetric turning biases., Comment: 32 pages, 17 figures

How do we capture the breadth of behavior in animal movement, from rapid body twitches to aging? Using high-resolution videos of the nematode worm $C. elegans$, we show that a single dynamics connects posture-scale fluctuations with trajectory diffusion, and longer-lived behavioral states. We take short posture sequences as an instantaneous behavioral measure, fixing the sequence length for maximal prediction. Within the space of posture sequences we construct a fine-scale, maximum entropy partition so that transitions among microstates define a high-fidelity Markov model, which we also use as a means of principled coarse-graining. We translate these dynamics into movement using resistive force theory, capturing the statistical properties of foraging trajectories. Predictive across scales, we leverage the longest-lived eigenvectors of the inferred Markov chain to perform a top-down subdivision of the worm's foraging behavior, revealing both "runs-and-pirouettes" as well as previously uncharacterized finer-scale behaviors. We use our model to investigate the relevance of these fine-scale behaviors for foraging success, recovering a trade-off between local and global search strategies., Comment: 28 pages, 15 figures

In this work, we compared the effect of Quartzite nanoparticles (QtzNP - crystalline SiO$_2$) and amorphous silica nanoparticles (ASNP) as scatters in a random laser (RL), correlating the laser efficiency to the morphology and refractive index (RI) of the scatterers. The RL was based on a laser media containing suspensions of QtzNPs or ASNPs in Rhodamine 6G (Rh6G) and ethylene glycol (EG) suspension. It was observed a considerable increase in RL efficiency for QtzNPs, as compared to ASNPs, even for concentrations as low as 0.5mg/mL. Such grow in the RL eficiency is attributed to the higher RI of QtzNPs (n=1.54), which in-creases the reflectance of light on the particles surface and the high field scattering intensity in the sharp edges of the flat slab shapes, associated to the particle's morphology. Finite Element Method (FEM) simu-lations were also performed for different particle size and shapes and an output increase is noticed for QtzNPs when compared with the ASNP confirming the experimental results. The comparison between the morphology of QtzNPs and ASNPs on scattering efficiency reported here contribute to optimize the performance of laser systems with natural and synthetic nanomaterials.

Engineering knowledge-based (or expert) systems require extensive manual effort and domain knowledge. As Large Language Models (LLMs) are trained using an enormous amount of cross-domain knowledge, it becomes possible to automate such engineering processes. This paper presents an empirical automation and semi-automation framework for domain knowledge distillation using prompt engineering and the LLM ChatGPT. We assess the framework empirically in the autonomous driving domain and present our key observations. In our implementation, we construct the domain knowledge ontology by "chatting" with ChatGPT. The key finding is that while fully automated domain ontology construction is possible, human supervision and early intervention typically improve efficiency and output quality as they lessen the effects of response randomness and the butterfly effect. We, therefore, also develop a web-based distillation assistant enabling supervision and flexible intervention at runtime. We hope our findings and tools could inspire future research toward revolutionizing the engineering of knowledge-based systems across application domains., Comment: Accepted by ITSC 2023

The transfer of information between two physical locations is an essential component of both classical and quantum computing. In quantum computing the transfer of information must be coherent to preserve quantum states and hence the quantum information. We establish a simple protocol for transferring one- and two-electron encoded logical qubits in quantum dot arrays. The theoretical energetic cost of this protocol is calculated - in particular, the cost of freezing and unfreezing tunnelling between quantum dots. Our results are compared with the energetic cost of shuttling qubits in quantum dot arrays and transferring classical information using classical information buses. Only our protocol can manage constant dissipation for any chain length. This protocol could reduce the cooling requirements and constraints on scalable architectures for quantum dot quantum computers., Comment: 10 pages, 6 figures

Animal behavior is shaped by a myriad of mechanisms acting on a wide range of scales, which hampers quantitative reasoning and the identification of general principles. Here, we combine data analysis and theory to investigate the relationship between behavioral plasticity and heavy-tailed statistics often observed in animal behavior. Specifically, we first leverage high-resolution recordings of C. elegans locomotion to show that stochastic transitions among long-lived behaviors exhibit heavy-tailed first passage time distributions and correlation functions. Such heavy tails can be explained by slow adaptation of behavior over time. This particular result motivates our second step of introducing a general model where we separate fast dynamics on a quasi-stationary multi-well potential, from non-ergodic, slowly varying modes. We then show that heavy tails generically emerge in such a model, and we provide a theoretical derivation of the resulting functional form, which can become a power law with exponents that depend on the strength of the fluctuations. Finally, we provide direct support for the generality of our findings by testing them in a C. elegans mutant where adaptation is suppressed and heavy tails thus disappear, and recordings of larval zebrafish swimming behavior where heavy tails are again prevalent., Comment: 24 pages, 13 figures

A knot $K$ in $S^3$ is $q$-periodic if it admits a symmetry that is conjugate to a rotation of order $q$ of $S^3$. If $K$ admits a symmetry which is a homeomorphism without fixed point of period $q$ of $S^3$, then $K$ is called freely $q$-periodic. In a previous paper, we obtained, as a consequence of Flyping Theorem due to Menasco and Thislethwaite, that the $q$-periodicity with $q>2$ can be visualized in an alternating projection as a rotation of the projection sphere. In this paper, we show that the free $q$-action of an alternating knot can be represented on some alternating projection as a composition of a rotation of order $q$ with some flypes all occurring on the same twisted band diagram of its essential Conway decomposition. Therefore, for an alternating knot to be freely periodic, its essential decomposition must satisfy certain conditions. We show that any free or non-free $q$-action is somehow visible (virtually visible) and give some sufficient criteria to detect the existence of $q$-actions from virtually visible projections. Finally, we show how the Murasugi decomposition into atoms enables us to determine the visibility type $(q,r)$ of the freely $q$-periodic alternating knots ($(q,r)$-lens knots); in fact, we only need to focus on a certain atom of their Murasugi decomposition to deduce their visibility type.

We present a proposal for a one-bit full-adder to process classical information based on the quantum reversible dynamics of a triple quantum dot system. The device works via the repeated execution of a Fredkin gate implemented through the dynamics of a single time-independent Hamiltonian. Our proposal uses realistic parameter values and could be implemented on currently available quantum dot architectures. We compare the estimated energy requirements for operating our full-adder with those of well-known fully classical devices, and argue that our proposal may provide a consistently better energy efficiency. Our work serves as a proof of principle for the development of energy-efficient information technologies operating through coherent quantum dynamics., Comment: V2: Minor updates. -- Keywords: energy-efficient computing, quantum dynamics, quantum gates, semiconductor quantum dots, quantum technologies