Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study

In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e., the double-triangle diagram and the triangle-box diagram. For later two kinds of diagrams, we have given complete analytical results in general (4-2\eps)-dimension.Comment: 52 pages, 1 figur

Development of a Small Intelligent Weather Station for Agricultural Applications

It is known that climate change causes a decrease in the profit gained from agricultural production. This work designs and establishes weather boxes equipped with functions of rainfall prediction, frosting forecast, and lightning detection. With the wireless connection and the build-in decision mode, weather boxes can deliver early-warning by sending texting messages to the users and actuating the corresponding action to response the extreme climate. To implement rainfall and frosting prognostication, two different datasets are analyzed by the technology of data mining. One of the datasets is acquired from the Central Weather Bureau, and the other is from the proposed weather box monitoring the agricultural environment. From the experimental results, the prediction model constructed from the data which is collected by the proposed weather box exhibits a higher accuracy in rainfall forecasting than those based on the Central Weather Bureau

Distribution of equilibrium free energies in a thermodynamic system with broken ergodicity

At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $\Omega_s \sim \exp({\rm const} \times N)$ of ergodic sub-spaces (thermodynamic states). Previous theoretical studies assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density, and that the equilibrium free energies follow the distribution of exponential decay. Here we show that these assumptions are not necessarily valid. For some complex systems, the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range, and consequently their equilibrium properties are contributed by {\em excited} thermodynamic states. This work will help improving our understanding of the equilibrium statistical mechanics of spin-glasses and other complex systems.Comment: 7 pages, 2 figure

Density functional theory based neural network force fields from energy decompositions

In order to develop force fields (FF) for molecular dynamics simulations that retain the accuracy of ab initio density functional theory (DFT), we developed a machine learning protocol based on an energy decomposition scheme that extracts atomic energies from DFT calculations. Our DFT to FF (DFT2FF) approach provides almost hundreds of times more data for the DFT energies, which dramatically improves accuracy with less DFT calculations. In addition, we use piecewise cosine basis functions to systematically construct symmetry invariant features into the neural network model. We illustrate this DFT2FF approach for amorphous silicon where only 800 DFT configurations are sufficient to achieve an accuracy of 1 meV/atom for energy and 0.1 eV/A for forces. We then use the resulting FF model to calculate the thermal conductivity of amorphous Si based on long molecular dynamics simulations. The dramatic speedup in training in our DFT2FF protocol allows the adoption of a simulation paradigm where an accurate and problem specific FF for a given physics phenomenon is trained on-the-spot through a quick DFT precalculation and FF training

Observation of a linear temperature dependence of the critical current density in a Ba_{0.63}K_{0.37}BiO_3 single crystal

For a Ba_{0.63}K_{0.37}BiO_3 single crystal with T_c=31 K, H_{c1}=750 Oe at 5 K, and dimensions 3x3x1 mm^3, the temperature and field dependences of magnetic hysteresis loops have been measured within 5-25 K in magnetic fields up to 6 Tesla. The critical current density is J_c(0)=1.5 x 10^5 A/cm^2 at zero field and 1 x 10^5 A/cm^2 at 1 kOe at 5 K. J_c decreases exponentially with increasing field up to 10 kOe. A linear temperature dependence of J_c is observed below 25 K, which differs from the exponential and the power-law temperature dependences in high-Tc superconductors including the BKBO. The linear temperature dependence can be regarded as an intrinsic effect in superconductors.Comment: RevTex, Physica C Vol. 341-348, 729 (2000

Stochastic Linear-quadratic Control Problems with Affine Constraints

In this paper, we investigate the stochastic linear-quadratic control problems with affine constraints in random coefficients case. With the help of the Pontryagin maximum principle and stochastic Riccati equation, the dual problem of original problem is established and the feedback solution of the optimal control problem is obtained. Under the Slater condition, the equivalence is proved between the solutions to the original problem and the ones of the dual problem, and the KKT condition is also provided for the dual problem. Finally, an invertibility assumption is given for ensuring the uniqueness of the solutions to the dual problem

S3Eval: A Synthetic, Scalable, Systematic Evaluation Suite for Large Language Models

The rapid development of Large Language Models (LLMs) has led to great strides in model capabilities like reasoning and long-context understanding. However, as LLMs are able to process longer contexts, it becomes more challenging to evaluate whether they have acquired certain capabilities, since the length of text (e.g., 100K tokens) they can process far exceeds what humans can reliably assess in a reasonable duration. In this paper, we propose using complex synthetic tasks as a proxy evaluation method, and present S3Eval, a Synthetic, Scalable, Systematic evaluation suite for LLMs evaluation. As a synthetic benchmark, S3Eval enables the creation of any number of evaluation examples that are theoretically invisible to LLMs, mitigating the test set contamination issue. The synthetic nature of S3Eval provides users full control over the dataset, allowing them to systematically probe LLM capabilities by scaling text length and varying task difficulty across diverse scenarios. The strong correlation between S3Eval performance and scores of real-world benchmarks like Big-Bench Hard (BBH) demonstrates the soundness of using S3Eval for evaluation of LLMs. The in-depth analysis also uncover additional insights, including performance drop when the answer is sparsely distributed or located in the middle context, as well as some counter-intuitive trends of model performance.Comment: Work in progres

4-[(2′-Cyano­biphen­yl-4-yl)meth­yl]morpholin-4-ium tetra­fluoridoborate

In the crystal structure of the title compound, C18H19N2O+·BF4 −, bifurcated N—H⋯(F,F) hydrogen bonds link the protonated 4′-morpholine­methyl­biphenyl-2-carbonitrile cations and slightly distorted tetra­fluoro­borate anions. π–π inter­actions [centroid–centroid distance = 3.805 (3) Å] help to consolidate the packing. The dihedral angle between the benzene rings in the cation is 57.24 (11)°