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Reconstructing a parsimonious phylogenetic network that displays multiple phylogenetic trees is an important problem in theory of phylogenetics, where the complexity of the inferred networks is measured by reticulation numbers. The reticulation number for a set of trees is defined as the minimum number of reticulations in a phylogenetic network that displays those trees. A mathematical problem is bounding the reticulation number for multiple trees over a fixed number of taxa. While this problem has been extensively studied for two trees, much less is known about the upper bounds on the reticulation numbers for three or more arbitrary trees. In this paper, we present a few non-trivial upper bounds on reticulation numbers for three or more trees., Comment: 9 figures, 18 pages

We propose a machine learning pipeline for forensic shoeprint pattern matching that improves on the accuracy and generalisability of existing methods. We extract 2D coordinates from shoeprint scans using edge detection and align the two shoeprints with iterative closest point (ICP). We then extract similarity metrics to quantify how well the two prints match and use these metrics to train a random forest that generates a probabilistic measurement of how likely two prints are to have originated from the same outsole. We assess the generalisability of machine learning methods trained on lab shoeprint scans to more realistic crime scene shoeprint data by evaluating the accuracy of our methods on several shoeprint scenarios: partial prints, prints with varying levels of blurriness, prints with different amounts of wear, and prints from different shoe models. We find that models trained on one type of shoeprint yield extremely high levels of accuracy when tested on shoeprint pairs of the same scenario but fail to generalise to other scenarios. We also discover that models trained on a variety of scenarios predict almost as accurately as models trained on specific scenarios.

Superconducting diode effects have recently attracted much attention for their potential applications in superconducting logic circuits. Several mechanisms such as magneto-chiral effects, finite momentum Cooper pairing, asymmetric edge currents have been proposed to give rise to a supercurrent diode effect in different materials. In this work, we establish the presence of a large intrinsic Josephson diode effect in a type-II Dirac semimetal $1T-PtTe_2$ facilitated by its helical spin-momentum locking and distinguish it from other extrinsic effects. The magnitude of the Josephson diode effect is shown to be directly correlated to the large second-harmonic component of the supercurrent that is induced by the significant contribution of the topological spin-momentum locked states that promote coherent Andreev processes in the junction. We denote such junctions, where the relative phase between the two harmonics corresponding to charge transfers of $2e$ and $4e$ can be tuned by a magnetic field, as second order ${\phi}_0$-junctions. The direct correspondence between the second harmonic supercurrent component and the diode effect in $1T-PtTe_2$ junctions makes topological semimetals with high transparency an ideal platform to study and implement the Josephson diode effect, while also enabling further research on higher order supercurrent transport in Josephson junctions.

Reinforcement learning is an emerging approaches to facilitate multi-stage sequential decision-making problems. This paper studies a real-time multi-stage stochastic power dispatch considering multivariate uncertainties. Current researches suffer from low generalization and practicality, that is, the learned dispatch policy can only handle a specific dispatch scenario, its performance degrades significantly if actual samples and training samples are inconsistent. To fill these gaps, a novel contextual meta graph reinforcement learning (Meta-GRL) for a highly generalized multi-stage optimal dispatch policy is proposed. Specifically, a more general contextual Markov decision process (MDP) and scalable graph representation are introduced to achieve a more generalized multi-stage stochastic power dispatch modeling. An upper meta-learner is proposed to encode context for different dispatch scenarios and learn how to achieve dispatch task identification while the lower policy learner learns context-specified dispatch policy. After sufficient offline learning, this approach can rapidly adapt to unseen and undefined scenarios with only a few updations of the hypothesis judgments generated by the meta-learner. Numerical comparisons with state-of-the-art policies and traditional reinforcement learning verify the optimality, efficiency, adaptability, and scalability of the proposed Meta-GRL.

In contemporary society, the escalating pressures of life and work have propelled psychological disorders to the forefront of modern health concerns, an issue that has been further accentuated by the COVID-19 pandemic. The prevalence of depression among adolescents is steadily increasing, and traditional diagnostic methods, which rely on scales or interviews, prove particularly inadequate for detecting depression in young people. Addressing these challenges, numerous AI-based methods for assisting in the diagnosis of mental health issues have emerged. However, most of these methods center around fundamental issues with scales or use multimodal approaches like facial expression recognition. Diagnosis of depression risk based on everyday habits and behaviors has been limited to small-scale qualitative studies. Our research leverages adolescent census data to predict depression risk, focusing on children's experiences with depression and their daily life situations. We introduced a method for managing severely imbalanced high-dimensional data and an adaptive predictive approach tailored to data structure characteristics. Furthermore, we proposed a cloud-based architecture for automatic online learning and data updates. This study utilized publicly available NSCH youth census data from 2020 to 2022, encompassing nearly 150,000 data entries. We conducted basic data analyses and predictive experiments, demonstrating significant performance improvements over standard machine learning and deep learning algorithms. This affirmed our data processing method's broad applicability in handling imbalanced medical data. Diverging from typical predictive method research, our study presents a comprehensive architectural solution, considering a wider array of user needs.

Parametric down-conversion is a widely exploited technique in optics to produce entangled states of photons for quantum information processing and quantum sensing. In the microwave domain, devices based on Josephson junctions, such as Josephson parametric amplifiers (JPAs) and voltage-biased Josephson junctions, have been successfully utilized to generate such states. However, their high susceptibility to magnetic fields has posed challenges in many applications. Here we demonstrate the generation of two-mode squeezed states via four-wave-mixing in a superconducting nanowire resonator patterned from NbN. The NbN nanowire exhibits a strong Kerr nonlinearity, resulting in the emission of a signal-idler pair with a cross-correlation of $g^{(2)}(0) = 11.9$. Owing to the magnetic resilience and high critical temperature ($T_c$) of NbN, our microwave parametric sources based on kinetic inductance promise an expanded range of potential applications.

Superconducting microwave amplifiers are essential for sensitive signal readout in superconducting quantum processors. Typically based on Josephson Junctions, these amplifiers require operation at milli-Kelvin temperatures to achieve quantum-limited performance. Here we demonstrate a quantum microwave amplifier that employs radiative cooling to operate at elevated temperatures. This kinetic-inductance-based parametric amplifier, patterned from a single layer of high-$T_\mathrm{c}$ NbN thin film\cmt{in the form of a nanobridge}, maintains a high gain and meanwhile enables low added noise of 1.3 quanta when operated at 1.5 Kelvin. Remarkably, this represents only a 0.2 quanta increase compared to the performance at a base temperature of 0.1 Kelvin. By uplifting the parametric amplifiers from the mixing chamber without compromising readout efficiency, this work represents an important step for realizing scalable microwave quantum technologies.

Two dimensional van der Waals heterostructures (2D are of significant interest due to their intriguing physical properties that are critically defined by the constituent monolayers and their interlayer coupling . However, typical inorganic 2 D vdWhs fall into the weakly coupled region, limiting efficient interfacial charge flow crucial for developing high performance quantum opto electronics. Here, we demonstrate strong interlayer coupling in Cu3 BHT (BHT = benzenehexathiol) graphene vdWhs an organic inorganic bilayer characterized by prominent interlayer charge transfer Monolayer Cu3 BHT with a Kagome lattice is synthesized on the water surface and then coupled with graphene to produce a cm2 scale 2D vdWh. Spectroscopic and electrical studies, along with theoretical calculation s show significant hole transfer from monolayer Cu3 BHT to graphene upon contact , being characteristic fingerprints for strong interlayer coupling This study unveils the great potential of integrating highly pi-conjugated 2D coordination polymers (2DCPs) into 2D vdWhs to explor e intriguing physical phenomena.

This paper studies the value of a firm's internal information when the firm faces an adverse selection problem arising from unobservable managerial abilities. While more precise information allows the firm to make ex post more efficient investment decisions, noisier information has an ex ante screening effect that allows the firm to attract on-average better managers. The trade-off between more effective screening of managers and more informed investment implies a non-monotonic relationship between firm value and information quality. A marginal improvement in information quality does not necessarily lead to an overall improvement in firm value., Comment: Also available on SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3775306

Let $t \geq 2$ be an integer and $C(b,D)$ be a generalized Cantor set with $b \geq 3$. We study how close can numbers in $C(b,D)$ be approximated by rational numbers with denominators $t^n$. For any function $\psi : \mathbb{N} \to (0,\infty)$, let $W_{t} (\psi)$ be the set of numbers in $[0,1]$ such that $|x - p/t^n| < \psi(n)$ for infinitely many $(p,n) \in \mathbb{N}^2$. We correct an error in a result of Levesley, Salp and Velani (Math. Ann., 338:97-118, 2007) on the Hausdorff measure of $W_{t} (\psi) \cap C(b,D)$ when $b=t$, and also prove a generalization when $b$ and $t$ are multiplicatively dependent. If $b$ and $t$ are multiplicatively independent but have the same prime divisors, we obtain a partial result on the Hausdorff measure and bounds for the Hausdorff dimension, which are close to the multiplicatively dependent case. Based on these results, several conjectures are proposed.

The reconstruction of phylogenetic networks is an important but challenging problem in phylogenetics and genome evolution, as the space of phylogenetic networks is vast and cannot be sampled well. One approach to the problem is to solve the minimum phylogenetic network problem, in which phylogenetic trees are first inferred, then the smallest phylogenetic network that displays all the trees is computed. The approach takes advantage of the fact that the theory of phylogenetic trees is mature and there are excellent tools available for inferring phylogenetic trees from a large number of biomolecular sequences. A tree-child network is a phylogenetic network satisfying the condition that every non-leaf node has at least one child that is of indegree one. Here, we develop a new method that infers the minimum tree-child network by aligning lineage taxon strings in the phylogenetic trees. This algorithmic innovation enables us to get around the limitations of the existing programs for phylogenetic network inference. Our new program, named ALTS, is fast enough to infer a tree-child network with a large number of reticulations for a set of up to 50 phylogenetic trees with 50 taxa that have only trivial common clusters in about a quarter of an hour on average., Comment: 44 pages, 15 figures

Superconducting parametric amplifiers are crucial components in microwave quantum circuits for enabling quantum-limited signal readout. The best-performing such amplifiers are often based on Josephson junctions, which however are sensitive to magnetic fields. Therefore, they require magnetic shields and are not easily integratable with other quantum systems that operates within magnetic fields, such as spin ensemble quantum memories. To tackle this challenge, we have developed a kinetic inductance-based parametric amplifier featuring a NbN nanobridge instead of Josephson Junctions, which provides the desired nonlinearity for a strong parametric gain up to 42 dB. The added noise of this nanobridge kinetic-inductance parametric amplifier (hereby referred as NKPA) is calibrated and found to be $0.59\pm 0.03$ quanta for phase-preserving amplification, approaching the quantum limit of 0.5 quanta. Most importantly, we show that such excellent noise performance is preserved in an in-plane magnetic field up to 427 mT, the maximum field available in our experiment. This magnetic field-resilient parametric amplifier presents an opportunity towards addressing single electron-spin resonance and more efficient search for Axions as well as Majorana Fermions., Comment: Article, 8 pages, 3 figures

A binary phylogenetic network on a taxon set $X$ is a rooted acyclic digraph in which the degree of each nonleaf node is three and its leaves (i.e.degree-one nodes) are uniquely labeled with the taxa of $X$. It is tree-child if each nonleaf node has at least one child of indegree one. A set of binary phylogenetic trees may or may not be simultaneously displayed in a binary tree-child network. Necessary conditions for multiple phylogenetic trees being simultaneously displayed in a tree-child network are given here. In particular, it is proved that any two phylogenetic trees can always simultaneously be displayed in some tree-child network on the same taxa set. It is also proved that any set of multiple binary phylogenetic trees can always simultaneously be displayed in some non-binary tree-child network on the same taxa set, where each nonleaf node is of either indegree one and outdegree two or indegree at least two and outdegree out., Comment: 17 pages, 7 figures

Let $b \geq 2$ be an integer and $S$ be a finite non-empty set of primes not containing divisors of $b$. For any non-dense set $A \subset [0,1)$ such that $A \cap \mathbb{Q}$ is invariant under $\times b$ operation, we prove the finiteness of rational numbers in $A$ whose denominators can only be divided by primes in $S$. A quantitative result on the largest prime divisors of the denominators of rational numbers in $A$ is also obtained.

We investigate the magnetic symmetry of the topological antiferromagnetic material Mn$_3$Ge by using torque measurements. Below the Neel temperature, detailed angle-dependent torque measurements were performed on Mn$_3$Ge single crystals in directions parallel and perpendicular to the Kagome basal plane. The out-of plane torque data exhibit $\pm\sin\theta$ and $\sin2\theta$ behaviors, of which the former results from the spontaneous ferromagnetism within the basal plane and the latter from the in- and out-of-plane susceptibility anisotropy. The reversible component of the in-plane torque exhibits $\sin6\varphi$ behavior, revealing the six-fold symmetry of the in-plane magnetic free energy. Moreover, we find that the free energy minima are pinned to the direction of spontaneous ferromagnetism, which correspond to the maxima of the irreversible component of the in-plane torque. We provide an effective spin model to describe the in-plane magnetic anisotropy. Our results demonstrate that the ground state of Mn$_3$Ge is described by the coexistence of a strong six-fold antichiral order and a weak ferromagnetic order induced by second-order spin anisotropy.