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In this paper, we study the existence and properties of conformal measures on limit sets of (anti)holomorphic correspondences. We show that if the critical exponent satisfies $1\leq \delta_{\operatorname{crit}}(x) <+\infty,$ the correspondence $F$ is (relatively) hyperbolic on the limit set $\Lambda_+(x)$, and $\Lambda_+(x)$ is minimal, then $\Lambda_+(x)$ admits a non-atomic conformal measure for $F$ and the Hausdorff dimension of $\Lambda_+(x)$ is strictly less than 2. As a special case, this shows that for a parameter $a$ in the interior of a hyperbolic component of the modular Mandelbrot set, the limit set of the Bullett--Penrose correspondence $F_a$ has a non-atomic conformal measure and its Hausdorff dimension is strictly less than 2. The same results hold for the LLMM correspondences, under some extra assumptions on its defining function $f$., Comment: 37 pages, 2 figures

Quantum computing, with its superior computational capabilities compared to classical approaches, holds the potential to revolutionize numerous scientific domains, including pharmaceuticals. However, the application of quantum computing for drug discovery has primarily been limited to proof-of-concept studies, which often fail to capture the intricacies of real-world drug development challenges. In this study, we diverge from conventional investigations by developing \rev{a hybrid} quantum computing pipeline tailored to address genuine drug design problems. Our approach underscores the application of quantum computation in drug discovery and propels it towards more scalable system. We specifically construct our versatile quantum computing pipeline to address two critical tasks in drug discovery: the precise determination of Gibbs free energy profiles for prodrug activation involving covalent bond cleavage, and the accurate simulation of covalent bond interactions. This work serves as a pioneering effort in benchmarking quantum computing against veritable scenarios encountered in drug design, especially the covalent bonding issue present in both of the case studies, thereby transitioning from theoretical models to tangible applications. Our results demonstrate the potential of a quantum computing pipeline for integration into real world drug design workflows.

In this work, we investigate the Variational Principle and develop a thermodynamic formalism for correspondences. We define the measure-theoretic entropy for transition probability kernels and topological pressure for correspondences. Based on these two notions, we establish the following results: The Variational Principle holds and equilibrium states exist for continuous potential functions, provided that the correspondence satisfies some expansion property called forward expansiveness. If, in addition, the correspondence satisfies the specification property and the potential function is Bowen summable, then the equilibrium state is unique. On the other hand, for a distance-expanding, open, strongly transitive correspondence and a H\"{o}lder continuous potential function, there exists a unique equilibrium state, and the backward orbits are equidistributed. Furthermore, we investigate the Variational Principle for general correspondences. In conformal dynamics, we establish the Variational Principle for the Lee--Lyubich--Markorov--Mazor--Mukherjee anti-holomorphic correspondences, which are matings of some anti-holomorphic rational maps with anti-Hecke groups and not forward expansive. We also show a Ruelle--Perron--Frobenius Theorem for a family of hyperbolic holomorphic correspondences of the form $\boldsymbol{f}_c (z)= z^{q/p}+c$., Comment: 100 pages. Reformatted, polished, Index added, typos corrected

We investigate the propagation of positive streamers in CO$_2$ through 3D particle-in-cell simulations, which are qualitatively compared against experimental results at 50 mbar. The experiments show that CO$_2$ streamers are much more stochastic than air streamers at the same applied voltage, indicating that few electrons are available in front of the streamer head. In the simulations, we include a photoionization model for CO$_2$. The computational results show that even a small amount of photoionization can sustain positive streamer propagation, but this requires a background electric field close to the critical field. When we compare streamers in CO$_2$ and in air at the same applied voltage, the electric field at the streamer head and the electron density in the streamer channel are higher in CO$_2$. We discuss the uncertainties in CO$_2$ photoionization and provide an estimate for the quenching pressure, which is based on the radiative lifetime of emitting states and the collision frequency of the gas. Furthermore, a criterion for self-sustained streamer growth in CO$_2$ is presented and compared against simulation results.

A sememe is defined as the minimum semantic unit of human languages. Sememe knowledge bases (KBs), which contain words annotated with sememes, have been successfully applied to many NLP tasks, and we believe that by learning the smallest unit of meaning, computers can more easily understand human language. However, Existing sememe KBs are built on only manual annotation, human annotations have personal understanding biases, and the meaning of vocabulary will be constantly updated and changed with the times, and artificial methods are not always practical. To address the issue, we propose an unsupervised method based on a deep clustering network (DCN) to build a sememe KB, and you can use any language to build a KB through this method. We first learn the distributed representation of multilingual words, use MUSE to align them in a single vector space, learn the multi-layer meaning of each word through the self-attention mechanism, and use a DNC to cluster sememe features. Finally, we completed the prediction using only the 10-dimensional sememe space in English. We found that the low-dimensional space can still retain the main feature of the sememes., Comment: 6 pages, 6 figures, published to SIG-SLUD

We study negative streamers in ambient air using a 2D axisymmetric fluid model. Depending on the background electric field, we observe accelerating, steady and fading negative streamers. Fading occurs in low background fields, when negative streamers lose their field enhancement and when their velocities become comparable to their maximal electron drift velocities. Our focus is on the steady propagation mode, during which streamer properties like radius and velocity hardly change. However, this mode is unstable, in the sense that a small change in conditions leads to acceleration or deceleration. We observe steady negative streamers in background fields ranging from 9.19 kV/cm to 15.75 kV/cm, indicating that there is no unique steady propagation field (or stability field). Another finding is that steady negative streamers are able to keep propagating over tens of centimeters, with only a finite conductive length behind their heads, similar to steady positive streamers. Approximately linear relationships are observed between the optical diameter and properties like the streamer velocity and the streamer head potential. From these linear relations, we obtain rough lower bounds of about 0.27 mm to 0.35 mm for the minimal optical diameter of steady negative streamers. The lowest background field in which a steady negative streamer could be obtained is 9.19 kV/cm. In contrast, steady positive streamers have recently been obtained in a background field as low as 4.05 kV/cm. We find that the properties of steady negative and positive streamers differ significantly. For example, for steady negative streamers the ratio between streamer velocity and maximal electron drift velocity ranges from about 2 to 4.5, whereas for steady positive streamers this ratio ranges from about 0.05 to 0.26.

In this paper, we address two main topics: steady propagation fields for positive streamers in air and streamer deceleration in fields below the steady propagation field. We generate constant-velocity positive streamers in air with an axisymmetric fluid model, by initially adjusting the applied voltage based on the streamer velocity. After an initial transient, we observe steady propagation for velocities of $3\times10^4$ m/s to $1.2\times10^5$ m/s, during which streamer properties and the background field do not change. This propagation mode is not fully stable, in the sense that a small change in streamer properties or background field eventually leads to acceleration or deceleration. An important finding is that faster streamers are able to propagate in significantly lower background fields than slower ones, indicating that there is no unique stability field. We relate the streamer radius, velocity, maximal electric field and background electric field to a characteristic time scale for the loss of conductivity. This relation is qualitatively confirmed by studying streamers in N2-O2 mixtures with less oxygen than air. In such mixtures, steady streamers require lower background fields, due to a reduction in the attachment and recombination rates. We also study the deceleration of streamers, which is important to predict how far they can propagate in a low field. Stagnating streamers are simulated by applying a constant applied voltage. We show how the properties of these streamers relate to the steady cases, and present a phenomenological model with fitted coefficients that describes the evolution of the velocity and radius. Finally, we compare the lengths of the stagnated streamers with predictions based on the conventional stability field.