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Self-similar dynamics, often described by partial differential equations (PDEs) without noise terms, have been widely observed in nature and have attracted considerable attention from researchers in various fields, including physics, fluid mechanics, applied mathematics, and chemical engineering. The concept of universality class and the renormalization group (RG) theory, emerged from critical phenomena, which also have been widely observed in nature, are pillars of modern physics, with guiding the recent development of physics. While self-similarity appearing in fluid dynamics reminds physicists of critical phenomena, deep connections between them have not been explored. Here, we focus on a variation of a daily phenomenon, a drop falling from a faucet, and demonstrate self-similar dynamics for the shape of liquid-air interface in confined space with a scaling law for a characteristic length scale, which leads to a clear correspondence between the present self-similar dynamics and critical phenomena by identifying critical exponents, which define a universality class. We not only show that the observed master curve describing the self-similar shape is a solution to the Navier-Stokes equations, but also develop a renormalization group (RG) theory for the governing PDE to show the fixed point of RG corresponds to the solution, which becomes stable with time due to a scaling crossover. Our results will impact on our understanding of critical, scaling, and singular behaviors widely observed in nature.

Transformer has been adopted to image recognition tasks and shown to outperform CNNs and RNNs while it suffers from high training cost and computational complexity. To address these issues, a hybrid approach has become a recent research trend, which replaces a part of ResNet with an MHSA (Multi-Head Self-Attention). In this paper, we propose a lightweight hybrid model which uses Neural ODE (Ordinary Differential Equation) as a backbone instead of ResNet so that we can increase the number of iterations of building blocks while reusing the same parameters, mitigating the increase in parameter size per iteration. The proposed model is deployed on a modest-sized FPGA device for edge computing. The model is further quantized by QAT (Quantization Aware Training) scheme to reduce FPGA resource utilization while suppressing the accuracy loss. The quantized model achieves 79.68% top-1 accuracy for STL10 dataset that contains 96$\times$96 pixel images. The weights of the feature extraction network are stored on-chip to minimize the memory transfer overhead, allowing faster inference. By eliminating the overhead of memory transfers, inference can be executed seamlessly, leading to accelerated inference. The proposed FPGA implementation accelerates the backbone and MHSA parts by 34.01$\times$, and achieves an overall 9.85$\times$ speedup when taking into account the software pre- and post-processing. The FPGA acceleration leads to 7.10$\times$ better energy efficiency compared to the ARM Cortex-A53 CPU. The proposed lightweight Transformer model is demonstrated on Xilinx ZCU104 board for the image recognition of 96$\times$96 pixel images in this paper and can be applied to different image sizes by modifying the pre-processing layer.

Ecosystems, which are intricate amalgams of biological communities and their surrounding environments, continually evolve under the influence of their myriad interactions. The world is currently facing intensifying environmental fluctuations. Understanding general trends in ecosystem transformations in response to environmental fluctuations and elucidating the underlying mechanisms are thus critical challenges. In this study, we used a model ecosystem approach to investigate ecosystem alterations caused by escalating environmental fluctuations. We analyzed two distinct models: a stochastic ecosystem model with a spatial structure, and a differential equation model for resource competition. We found that environmental fluctuations tend to shift multi-species coexistence toward the dominance of specific species. We also categorized biological species as specialists or generalists and discovered that which of these groups becomes the dominant species depends on the intensity and frequency of environmental fluctuations. We also determined that a qualitative change in the diversity-stability relationship depends on the period of environmental fluctuations. These results underscore the need to explicitly consider the type of perturbation when discussing ecological transitions and the stability of ecosystems. Our findings advance understanding of the mechanisms underlying how environmental changes reshape ecosystems and offer insights into ecosystem sustainability in the face of future environmental perturbations., Comment: 9 pages, 4 figures

Low-Gain Avalanche Diode (LGAD) sensor is one of candidate sensors for the tracker at future hadron collider experiments. To use this sensor as a tracking detector, AC-LGAD sensor is being developed which has both timing and spatial resolutions. In high luminosity environments, good timing resolution (typically 30 ps) together with $\mathcal{O}$(10) ${\mathrm{\mu}}$m spatial resolution helps to reduce pileup effect and reconstruct tracks correctly. By optimizing fabrication parameters, 80 ${\mathrm{\mu}}$m pitch strip and 100 ${\mathrm{\mu}}$m pitch pixel sensors are successfully produced. The signal height (MPV) was 39.26$\pm$0.08 mV and 128.9$\pm$3.3 mV, respectively, for penetrating $\beta$ particles. The observed 60% of signal reduction of the strip sensor is explained by a larger inter-electrode capacitance compared with the pixel sensor. In this paper, we present the performance of fine electrode pitch AC-LGAD sensors including the pulse height and cross-talk of pixel and strip type sensors evaluated using a $\beta$-ray source and the detection efficiency measured in an 800 MeV electron beam., Comment: 8 pages, 6 figures, Submitted to Japan Conference Proceedings

We discuss basic potentials of the nonrelativistic and relativistic quantum mechanics that can be integrated in the Nikiforov and Uvarov paradigm with the aid of a computer algebra system. This consideration may help the readers to study analytical methods of quantum physics., Comment: 51 pages, 19 tables; 3 figures; complementary Mathematica notebook is available from the authors; It is also posted on Wolfram community https://community.wolfram.com/groups/-/m/t/2897057

In this paper, we prove the existence of a phase transition of parallelizability in the assembly of one-dimensional chains. By introducing the parallel efficiency that measures how efficiently the parallel assembly works, the parallelizable phase is defined by its positive value. The parallelizable/unparallelizable transition is then identified by the non-analytic change in the parallel efficiency from a positive value to zero. By evaluating the parallel efficiency on each side of the transition point, we show the existence of a phase transition in this system., Comment: This paper has been withdrawn by the authors. This paper has been superseded by arXiv:2302.00909 (merged from arXiv:2302.00909 and arXiv:2302.00914)

We propose a phase transition on the feasibility of efficient parallel assembly. By introducing the parallel efficiency that measures how efficiently the parallel assembly works, the parallelizable phase is defined by its positive value. The parallelizable/unparallelizable transition is then identified by the non-analytic change in the parallel efficiency from a positive value to zero. We present two analyzable models to demonstrate this phase transition in the limit of infinite system size., Comment: 11 pages, 12 figures

For classical discrete systems under constant composition (typically reffered to as substitutional alloys), canonical average phi typically provides a complicated nonlinear map from a set of potential energy surface to that of macroscropic structure in thermodynamic equilibrium, the so-called canonical nonlinearity: CN. Although our recent study reveals that the CN can be reasonablly addressed for individual microscopic configuration by two different ways of special vector field on configuration space, anharmonicity in the structural degree of freedoms (ASDF), and Kullback-Leibler (KL) divergence DKL, that is the conceptual extention of ASDF to statistical manifold to include further non-local information about CN, their direct correlation on real lattices, is still totally unclear. We here tuckle this problem for fcc-based equiatomic binary alloys that have been most studied in the CN-based context. We confirm that while one of the contribution to CN of DdG for each configuration, due to difference in CDOS from Gaussian, exhibits significant positive correlation with ASDF, another contribution of Dns due to non-separability in structural degee of freedoms (SDFs) exhibit no effective correlation with ASDF, which can be naturally accepted since the former contribution depends on ASDF itself, while the latter is independent. We find that average of Dns over all configurations for sets of SDFs can be well-characterized by information about asymmetric Hausdorff distance between configurational polyhedra (CP) for practical and ideally separable system, and CP hypervolumes. This fact certainly indicates that non-local information about CN has profound connection to the geometric configuration for ground-state structures of alloys on configuration space., Comment: 5 pages, 7 figures. Results for vector field on bcc lattice is added from previous version

The number of IoT devices is predicted to reach 125 billion by 2023. The growth of IoT devices will intensify the collisions between devices, degrading communication performance. Selecting appropriate transmission parameters, such as channel and spreading factor (SF), can effectively reduce the collisions between long-range (LoRa) devices. However, most of the schemes proposed in the current literature are not easy to implement on an IoT device with limited computational complexity and memory. To solve this issue, we propose a lightweight transmission-parameter selection scheme, i.e., a joint channel and SF selection scheme using reinforcement learning for low-power wide area networking (LoRaWAN). In the proposed scheme, appropriate transmission parameters can be selected by simple four arithmetic operations using only Acknowledge (ACK) information. Additionally, we theoretically analyze the computational complexity and memory requirement of our proposed scheme, which verified that our proposed scheme could select transmission parameters with extremely low computational complexity and memory requirement. Moreover, a large number of experiments were implemented on the LoRa devices in the real world to evaluate the effectiveness of our proposed scheme. The experimental results demonstrate the following main phenomena. (1) Compared to other lightweight transmission-parameter selection schemes, collisions between LoRa devices can be efficiently avoided by our proposed scheme in LoRaWAN irrespective of changes in the available channels. (2) The frame success rate (FSR) can be improved by selecting access channels and using SFs as opposed to only selecting access channels. (3) Since interference exists between adjacent channels, FSR and fairness can be improved by increasing the interval of adjacent available channels., Comment: 14 pages, 12 figures, 8 tables. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Capacitive-coupled Low-Gain Avalanche Diode (AC-LGAD) sensors are being developed for high-energy particle physics experiments as a detector which provides fast time information with fine spatial resolution. This paper describes optimizations of AC-LGAD sensor fabrication parameters, such as doping concentrations of the gain and electrode layers as well as the AC insulator capacitance, to realize $\mathcal{O}$(10)~\um{} spacial resolution, small charge cross talk to the neighboring electrodes, detection efficiency higher than 99\% at a 10$^{-4}$ fake rate and time resolution of about 30~ps. The radiation tolerance of the sensor is presented. In addition, further application to a device capable of visible and infra-red light detection is discussed., Comment: 11 pages, 25 figures, Submitted to Nuclear Instruments & Methods in physics research A (NIMA)