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1. Sharpen data-driven prediction rules of individual large earthquakes with aid of Fourier and Gauss

   https://doi.org/10.1038/s41598-023-43181-z  

   Cho, In Ho (December 2023, Scientific Reports)

   Abstract Predicting individual large earthquakes (EQs)’ locations, magnitudes, and timing remains unreachable. The author’s prior study shows that individual large EQs have unique signatures obtained from multi-layered data transformations. Via spatio-temporal convolutions, decades-long EQ catalog data are transformed into pseudo-physics quantities (e.g., energy, power, vorticity, and Laplacian), which turn into surface-like information via Gauss curvatures. Using these new features, a rule-learning machine learning approach unravels promising prediction rules. This paper suggests further data transformation via Fourier transformation (FT). Results show that FT-based new feature can help sharpen the prediction rules. Feasibility tests of large EQs ($$M\ge$$ $M\ge$6.5) over the past 40 years in the western U.S. show promise, shedding light on data-driven prediction of individual large EQs. The handshake among ML methods, Fourier, and Gauss may help answer the long-standing enigma of seismogenesis. 

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2. The Brown measure of the free multiplicative Brownian motion

   https://doi.org/10.1007/s00440-022-01142-z  

   Driver, Bruce K.; Hall, Brian; Kemp, Todd (October 2022, Probability Theory and Related Fields)

   Abstract The free multiplicative Brownian motion$$b_{t}$$ $b_t$is the large-Nlimit of the Brownian motion on$$\mathsf {GL}(N;\mathbb {C}),$$ $\mathrm{GL}(N;C),$in the sense of$$*$$ $\ast$-distributions. The natural candidate for the large-Nlimit of the empirical distribution of eigenvalues is thus the Brown measure of$$b_{t}$$ $b_t$. In previous work, the second and third authors showed that this Brown measure is supported in the closure of a region$$\Sigma _{t}$$ ${\Sigma }_t$that appeared in the work of Biane. In the present paper, we compute the Brown measure completely. It has a continuous density$$W_{t}$$ $W_t$on$$\overline{\Sigma }_{t},$$ ${\overline{\Sigma }}_t,$which is strictly positive and real analytic on$$\Sigma _{t}$$ ${\Sigma }_t$. This density has a simple form in polar coordinates:$$\begin{aligned} W_{t}(r,\theta )=\frac{1}{r^{2}}w_{t}(\theta ), \end{aligned}$$ $\begin{array}{c}{W}_t(r,\theta )=\frac{1}{r^2}{w}_t\left(\theta \right),\end{array}$where$$w_{t}$$ $w_t$is an analytic function determined by the geometry of the region$$\Sigma _{t}$$ ${\Sigma }_t$. We show also that the spectral measure of free unitary Brownian motion$$u_{t}$$ $u_t$is a “shadow” of the Brown measure of$$b_{t}$$ $b_t$, precisely mirroring the relationship between the circular and semicircular laws. We develop several new methods, based on stochastic differential equations and PDE, to prove these results. 

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3. Probing light scalars and vector-like quarks at the high-luminosity LHC

   https://doi.org/10.1140/epjc/s10052-025-14085-1  

   Qureshi, U S; Gurrola, A; Flórez, A; Rodriguez, C (April 2025, The European Physical Journal C)

   Abstract A model based on a$$U(1)_{T^3_R}$$ $U{\left(1\right)}_{T_R^3}$extension of the Standard Model can address the mass hierarchy between generations of fermions, explain thermal dark matter abundance, and the muon$$g - 2$$ $g-2$,$$R_{(D)}$$ $R_{\left(D\right)}$, and$$R_{(D^*)}$$ $R_{\left(D^{\ast }\right)}$anomalies. The model contains a light scalar boson$$\phi '$$ ${\varphi }^{\prime }$and a heavy vector-like quark$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$that can be probed at CERN’s large hadron collider (LHC). We perform a phenomenology study on the production of$$\phi '$$ ${\varphi }^{\prime }$and$${\chi }_u$$ ${\chi }_u$particles from proton–proton$$(\textrm{pp})$$ $\left(\text{pp}\right)$collisions at the LHC at$$\sqrt{s}=13.6$$ $\sqrt{s}=13.6$TeV, primarily through$$g{-g}$$ $g-g$and$$t{-\chi _\textrm{u}}$$ $t-{\chi }_{\text{u}}$fusion. We work under a simplified model approach and directly take the$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$and$$\phi '$$ ${\varphi }^{\prime }$masses as free parameters. We perform a phenomenological analysis considering$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$final states to b-quarks, muons, and neutrinos, and$$\phi '$$ ${\varphi }^{\prime }$decays to$$\mu ^+\mu ^-$$ ${\mu }^{+}{\mu }^{-}$. A machine learning algorithm is used to maximize the signal sensitivity, considering an integrated luminosity of 3000$$\text {fb}^{-1}$$ ${\text{fb}}^{-1}$. The proposed methodology can be a key mode for discovery over a large mass range, including low masses, traditionally considered difficult due to experimental constraints. 

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4. Reduction of the electroweak correlation in the PDF updating by using the forward–backward asymmetry of Drell–Yan process

   https://doi.org/10.1140/epjc/s10052-022-10280-6  

   Yang, Siqi; Fu, Yao; Liu, Minghui; Zhang, Renyou; Hou, Tie-Jiun; Wang, Chen; Yin, Hang; Han, Liang; Yuan, C. -P. (April 2022, The European Physical Journal C)

   Abstract We propose a new observable for the measurement of the forward–backward asymmetry$$(A_{FB})$$ $\left(A_{\mathrm{FB}}\right)$in Drell–Yan lepton production. At hadron colliders, the$$A_{FB}$$ $A_{\mathrm{FB}}$distribution is sensitive to both the electroweak (EW) fundamental parameter$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$, the weak mixing angle, and the parton distribution functions (PDFs). Hence, the determination of$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$and the updating of PDFs by directly using the same$$A_{FB}$$ $A_{\mathrm{FB}}$spectrum are strongly correlated. This correlation would introduce large bias or uncertainty into both precise measurements of EW and PDF sectors. In this article, we show that the sensitivity of$$A_{FB}$$ $A_{\mathrm{FB}}$on$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$is dominated by its average value around theZpole region, while the shape (or gradient) of the$$A_{FB}$$ $A_{\mathrm{FB}}$spectrum is insensitive to$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$and contains important information on the PDF modeling. Accordingly, a new observable related to the gradient of the spectrum is introduced, and demonstrated to be able to significantly reduce the potential bias on the determination of$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$when updating the PDFs using the same$$A_{FB}$$ $A_{\mathrm{FB}}$data. 

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5. Evidence of a liquid–liquid phase transition in H$$_2$$O and D$$_2$$O from path-integral molecular dynamics simulations

   https://doi.org/10.1038/s41598-022-09525-x  

   Eltareb, Ali; Lopez, Gustavo E.; Giovambattista, Nicolas (April 2022, Scientific Reports)

   Abstract We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H$$_2$$ ${}_2$O and D$$_2$$ ${}_2$O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density$$\rho (T)$$ $\rho \left(T\right)$, isothermal compressibility$$\kappa _T(T)$$ ${\kappa }_T\left(T\right)$, and self-diffusion coefficientsD(T) of H$$_2$$ ${}_2$O and D$$_2$$ ${}_2$O are in excellent agreement with available experimental data; the isobaric heat capacity$$C_P(T)$$ $C_P\left(T\right)$obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$_2$$ ${}_2$O and D$$_2$$ ${}_2$O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$ ${}_2$O and D$$_2$$ ${}_2$O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H$$_2$$ ${}_2$O, from PIMD simulations, is located at$$P_c = 167 \pm 9$$ $P_c=167\pm 9$ MPa,$$T_c = 159 \pm 6$$ $T_c=159\pm 6$ K, and$$\rho _c = 1.02 \pm 0.01$$ ${\rho }_c=1.02\pm 0.01$ g/cm$$^3$$ ${}^3$. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D$$_2$$ ${}_2$O is estimated to be$$P_c = 176 \pm 4$$ $P_c=176\pm 4$ MPa,$$T_c = 177 \pm 2$$ $T_c=177\pm 2$ K, and$$\rho _c = 1.13 \pm 0.01$$ ${\rho }_c=1.13\pm 0.01$ g/cm$$^3$$ ${}^3$. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water,$$P_c = 203 \pm 4$$ $P_c=203\pm 4$ MPa,$$T_c = 175 \pm 2$$ $T_c=175\pm 2$ K, and$$\rho _c = 1.03 \pm 0.01$$ ${\rho }_c=1.03\pm 0.01$ g/cm$$^3$$ ${}^3$). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of$$T_c$$ $T_c$for D$$_2$$ ${}_2$O and, particularly, H$$_2$$ ${}_2$O suggest that improved water models are needed for the study of supercooled water. 

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