Parameter Space Research Articles

Nested chirality and multimode transfer around exceptional points driven by external forces in electric circuits

Exceptional points (EPs) are non-Hermitian degeneracies or branch points where eigenvalues and their corresponding eigenvectors coalesce. Due to the complex non-trivial topology of Riemann surfaces associated with non-Hermitian Hamiltonians, the dynamical encirclement or proximity of EPs in parameter space has been shown to lead to some novel physical phenomena, such as the chiral modes modulations. However, in the previous studies on dynamically encircling EPs, tuning the chirality for applications requires periodic modulation of the system parameters. Here, we propose theoretically and demonstrate experimentally a way to generate EPs and realize asymmetric multimode switching by tuning external forces. The application of the external force achieves the effect of modifying the system parameters so that the dynamical encircling of the EPs can be easily realized. It is shown theoretically that nested chiral behavior and multimode transfer appear in a two-dimensional non-Hermitian higher-order topological insulator with twofold degenerate second-order EPs by tuning the external forces. Furthermore, we design and fabricate the corresponding circuit networks, and experimentally observe nested chiral behavior and multimode transfer. Our work opens up avenues for practical applications of the non-Hermitian physical phenomena.

Fiducial Inference in Linear Mixed-Effects Models

We develop a novel framework for fiducial inference in linear mixed-effects (LME) models, with the standard deviation of random effects reformulated as coefficients. The exact fiducial density is derived as the equilibrium measure of a reversible Markov chain over the parameter space. The density is equivalent in form to a Bayesian LME with noninformative prior, while the underlying fiducial structure adds new benefits to unify the inference of random effects and all other parameters in a neat and simultaneous way. Our fiducial LME needs no additional tests or statistics for zero variance and is more suitable for small sample sizes. In simulation and empirical analysis, our confidence intervals (CIs) are comparable to those based on Bayesian and likelihood profiling methods. And our inference for the variance of random effects has competitive power with the likelihood ratio test.

Distributions of Wide Binary Stars in Theory and in Gaia Data. I. Generalized Ambartsumian (1937) Approach and the Family of Power-law Distributions of Eccentricity

Abstract The orbital parameter space of wide, weakly bound binary stars has been shaped by the still poorly known circumstances of their formation, as well as by subsequent dynamical evolution in parent clusters and in the field. The advance of the Gaia mission astrometry takes statistical studies of wide stellar systems to an unprecedented level of precision and scope. On the theoretical side of the problem, the old approach proposed by Jeans and developed by Ambartsumian is revisited here. It is shown how certain simplifying assumptions about the phase density of binary systems in the framework of general copula distributions can lead to a family of analytical representations for the marginal distribution of orbital eccentricity, including accommodating and flexible power-law models. We further demonstrate the application of these models in forward Monte Carlo simulations of the measured motion angles between the relative velocity and separation vectors on the example of 170 K listed Gaia binary systems, providing inference in the intrinsic distribution of orbital eccentricity.

Autoencoder Reconstruction of Cosmological Microlensing Magnification Maps

Abstract Enhanced modeling of microlensing variations in light curves of strongly lensed quasars improves measurements of cosmological time delays, the Hubble Constant, and quasar structure. Traditional methods for modeling extragalactic microlensing rely on computationally expensive magnification map generation. With large data sets expected from wide-field surveys like the Vera C. Rubin Legacy Survey of Space and Time, including thousands of lensed quasars and hundreds of multiply imaged supernovae, faster approaches become essential. We introduce a deep-learning model that is trained on pre-computed magnification maps covering the parameter space on a grid of κ, γ, and s. Our autoencoder creates a low-dimensional latent space representation of these maps, enabling efficient map generation. Quantifying the performance of magnification map generation from a low dimensional space is an essential step in the roadmap to develop neural network-based models that can replace traditional feed-forward simulation at much lower computational costs. We develop metrics to study various aspects of the autoencoder generated maps and show that the reconstruction is reliable. Even though we observe a mild loss of resolution in the generated maps, we find this effect to be smaller than the smoothing effect of convolving the original map with a source of a plausible size for its accretion disk in the red end of the optical spectrum and larger wavelengths and particularly one suitable for studying the broad-line region of quasars. Used to generate large samples of on-demand magnification maps, our model can enable fast modeling of microlensing variability in lensed quasars and supernovae.

Integrated neuronetwork modeling of EEG for diagnostic disorders of brain activity

The article discusses the structured multistage modeling of EEG by means of applied mathematics to customize the input parameter space for neural network prediction. Also, the approaches and models are analyzed for their accuracy in determining the relevant signal features and adaptability to real data. The activity of potentials during brain activity is a biological process that depends on many factors and hides a space of parameters, the search for which and their definition can open us up to a new perspective on the nature and activity of the human brain. A rational way of obtaining data on brain activity is a non-invasive electroencephalogram, which registers the potential difference on the electrodes relative to the base. For further processing of the received data, it is necessary to remove noise and artifacts from them. In this work, a stan-dard algorithm of frequency filtering and filtering from noise caused by the power grid is used. After processing the data, an overview of mathematical models is offered, which with a certain degree of accuracy try to simulate the behavior of the signal or the peak moments of certain features. Added to this is the use of the LSTM model to predict the further behavior of the signal with the preliminary introduction of chaos into the model due to the modified activation function (Gaussian noise) and the input modeling of the weights.

Beyond the inert doublet: imprints of Scotogenic Yukawa interactions at FCC-ee

It is tempting to interpret the minuscule scale of neutrino masses as a symptom of its radiative origin. In light of the notable leap in precision expected at the Future Circular Collider, we explore areas of the parameter space that can simultaneously support the detectable Higgs-strahlung signal with parallel ones from forthcoming measurements in low-energy observables. We pinpoint the role that the extra fermions have in shaping a signal distinct from the pure Inert Doublet one. The details of the full one-loop computation and on-shell renormalization are presented. Both normal and inverted hierarchies for the radiatively generated neutrino masses and angles are investigated.

Fast gradient-free activation maximization for neurons in spiking neural networks

Elements of neural networks, both biological and artificial, can be described by their selectivity for specific cognitive features. Understanding these features is important for understanding the inner workings of neural networks. For a living system, such as a neuron, whose response to a stimulus is unknown and not differentiable, the only way to reveal these features is through a feedback loop that exposes it to a large set of different stimuli. The properties of these stimuli should be varied iteratively in order to maximize the neuronal response. To utilize this feedback loop for a biological neural network, it is important to run it quickly and efficiently in order to reach the stimuli that maximizes certain neurons’ activation with the least number of iterations possible. Here we present a framework with an efficient design for such a loop. We successfully tested it on an artificial spiking neural network (SNN), which is a model that simulates the asynchronous spiking activity of neurons in living brains. Our optimization method for activation maximization is based on the low-rank Tensor Train decomposition of the discrete activation function. The optimization space is the latent parameter space of images generated by SN-GAN or VQ-VAE generative models. To our knowledge, this is the first time that effective AM has been applied to SNNs. We track changes in the optimal stimuli for artificial neurons during training and show that highly selective neurons can form already in the early epochs of training and in the early layers of a convolutional spiking network. This formation of refined optimal stimuli is associated with an increase in classification accuracy. Some neurons, especially in the deeper layers, may gradually change the concepts they are selective for during learning, potentially explaining their importance for model performance. The source code of our framework, MANGO (for Maximization of neuronal Activation via Non-Gradient Optimization) is available on GitHub (https://github.com/iabs-neuro/mango)

Exploring quasi-periodic shrimps in the parameter space of a discrete-time food chain model.

Shrimps are islands of regularity within chaotic regimes in bi-parameter spaces of nonlinear dynamical systems. While the presence of periodic shrimps has been extensively reported, recent research has uncovered the existence of quasi-periodic shrimps. Compared to their periodic counterparts, quasi-periodic shrimps require a relatively higher-dimensional phase-space to come into existence and are also quite uncommon to observe. This Focus Issue contribution delves into the existence and intricate dynamics of quasi-periodic shrimps within the parameter space of a discrete-time, three-species food chain model. Through high-resolution stability charts, we unveil the prevalence of quasi-periodic shrimps in the system's unsteady regime. We extensively study the bifurcation characteristics along the two borders of the quasi-periodic shrimp. Our analysis reveals that along the outer border, the system exhibits transition to chaos via intermittency, whereas along the inner border, torus-doubling and torus-bubbling phenomena, accompanied by finite doubling and bubbling cascades, are observed. Another salient aspect of this work is the identification of quasi-periodic accumulation horizon and different quasi-periodic (torus) adding sequences for the self-distribution of infinite cascades of self-similar quasi-periodic shrimps along the horizon in certain parameter space of the system.

Uncertainty analysis method for diagnosing multi-point defects in urban drainage systems

Urban drainage system (UDS) plays a key role in city urbanization, where defective pipes can lead to seepage. Previous studies have identified the locations of defects in UDS using inverse optimization models. However, the unique optimal solution neglects uncertainty analysis, which may lead to misdiagnosis. In addition, the multi-point defect diagnosis has heavy computational burden due to high dimensional parameters space. To address these issues, this paper proposes a hybrid method that leverages the genetic algorithm (GA) to identify probable space, and then utilizes the adaptive Metropolis (AM) to provide an estimation of the posterior probability distribution (PPD). Firstly, a multi-population GA is employed for the maximum exploration within the model space. Then, AM algorithm is used to explore the final PPD of each pipe defect parameter. The metrics accuracy (ACC), Matthews correlation coefficient (MCC) and mean absolute error (MAE) are used to evaluate the diagnosis performance. A synthetic UDS case with randomized multi-point seepage scenarios is used to validate the method. Results indicate that the proposed hybrid method is effective in diagnosing multi-point defect, with 0.91, 0.78 of the hybrid method and 0.87, 0.69 of the DiffeRential Evolution Adaptive Metropolis method for the ACC and MCC, respectively. Meanwhile, the diagnosis speed has increased by 32%. The result PPD passes the 90% confidence interval validation. The proposed method can provide effective uncertainty analysis to reduce misdiagnosis of the traditional method.

Equilibrium of morphological units in anabranching rivers

AbstractAnabranching rivers are characterized by multiple sequences of interacting channels. These patterns consist of morphological units in the form of closed loops, with an upstream bifurcation controlling the partition of water and sediment fluxes, and a downstream confluence where the two anabranches reconnect. Bifurcation‐confluence loops can also be encountered in single‐thread rivers showing a transitional planform between meandering and anabranching, often associated with width oscillations and chute cutoffs. Individual channel loops display an average length that is proportional to the reach‐averaged bankfull depth of alluvial rivers. The existence of a characteristic length scale reflects a hydro‐morphodynamic interaction taking place between the constitutive elements of these morphological features, bifurcations and confluences. However, it is not clear why channel loops should organize themselves to attain a certain spatial scale, and how their planform shape is related to the morphodynamical processes governing the distribution of water and sediment between the anabranches. In this work we tackle these issues through a comparative analysis of theoretical findings and remotely sensed data from natural gravel‐bed and sand‐bed rivers. Two missing ingredients are included with respect to previous analyses: the case where one of the anabranches stops transporting sediment, and the case of loops with unequal lengths of the bifurcates. The theoretical model suggests that four distinct types of long‐term equilibrium states can be identified, depending on the reach‐averaged bankfull properties and on the planform shape of the loop. The comparison between model results and field data reveals that most of the observed river loops place themselves consistently in the region of the parameter space where theory predicts that both branches keep open in the long term.

From chimeras to extensive chaos in networks of heterogeneous Kuramoto oscillator populations.

Populations of coupled oscillators can exhibit a wide range of complex dynamical behavior, from complete synchronization to chimera and chaotic states. We can, thus, expect complex dynamics to arise in networks of such populations. Here, we analyze the dynamics of networks of populations of heterogeneous mean-field coupled Kuramoto-Sakaguchi oscillators and show that the instability that leads to chimera states in a simple two-population model also leads to extensive chaos in large networks of coupled populations. Formally, the system consists of a complex network of oscillator populations whose mesoscopic behavior evolves according to the Ott-Antonsen equations. By considering identical parameters across populations, the system contains a manifold of homogeneous solutions where all populations behave identically. Stability analysis of these homogeneous states provided by the master stability function formalism shows that non-trivial dynamics might emerge on a wide region of the parameter space for arbitrary network topologies. As examples, we first revisit the two-population case and provide a complete bifurcation diagram. Then, we investigate the emergent dynamics in large ring and Erdös-Rényi networks. In both cases, transverse instabilities lead to extensive space-time chaos, i.e., irregular regimes whose complexity scales linearly with the system size. Our work provides a unified analytical framework to understand the emergent dynamics of networks of oscillator populations, from chimera states to robust high-dimensional chaos.

Error-based efficient parameter space partitioning for mesh adaptation and local reduced order models

Error-based efficient parameter space partitioning for mesh adaptation and local reduced order models

Translation of the downstream ORF from bicistronic mRNAs by human cells: Impact of codon usage and splicing in the upstream ORF.

Biochemistry textbooks describe eukaryotic mRNAs as monocistronic. However, increasing evidence reveals the widespread presence and translation of upstream open reading frames preceding the "main" ORF. DNA and RNA viruses infecting eukaryotes often produce polycistronic mRNAs and viruses have evolved multiple ways of manipulating the host's translation machinery. Here, we introduce an experimental model to study gene expression regulation from virus-like bicistronic mRNAs in human cells. The model consists of a short upstream ORF and a reporter downstream ORF encoding a fluorescent protein. We have engineered synonymous variants of the upstream ORF to explore large parameter space, including codon usage preferences, mRNA folding features, and splicing propensity. We show that human translation machinery can translate the downstream ORF from bicistronic mRNAs, albeit reporter protein levels are thousand times lower than those from the upstream ORF. Furthermore, synonymous recoding of the upstream ORF exclusively during elongation significantly influences its own translation efficiency, reveals cryptic splice signals, and modulates the probability of downstream ORF translation. Our results are consistent with a leaky scanning mechanism facilitating downstream ORF translation from bicistronic mRNAs in human cells, offering new insights into the role of upstream ORFs in translation regulation.

Almost synchronization phenomena in the two and three coupled Brusselator systems

We present a study of some temporal almost synchronization phenomena of systems of two and three coupled Brusselators: they are approximately synchronized during most of the dynamics, only losing synchronization for small times and quickly returning to an almost synchronized state. Here we show two situations where this phenomenon occurs, one related with codimension-two Hopf-pitchfork bifurcations, and the other one due to the existence of fast-slow dynamics. On the one hand, a detailed characterization of the codimension-two Hopf-pitchfork bifurcations in the model allows us to determine the regions of the parameter space in which this phenomenon occurs. On the other hand, a fast-slow analysis of the two coupled Brusselators, using singular perturbation theory, illustrates the second situation studied here. We next analyze this phenomenon numerically, by explicitly calculating the fraction of time during which different trajectories are almost synchronized. Our results are then extended to the case of three coupled Brusselators.

Shining light on the dark sector: search for axion-like particles and other new physics in photonic final states with FASER

The first FASER search for a light, long-lived particle decaying into a pair of photons is reported. The search uses LHC proton-proton collision data at s = 13.6 TeV collected in 2022 and 2023, corresponding to an integrated luminosity of 57.7 fb−1. A model with axion-like particles (ALPs) dominantly coupled to weak gauge bosons is the primary target. Signal events are characterised by high-energy deposits in the electromagnetic calorimeter and no signal in the veto scintillators. One event is observed, compared to a background expectation of 0.44 ± 0.39 events, which is entirely dominated by neutrino interactions. World-leading constraints on ALPs are obtained for masses up to 300 MeV and couplings to the Standard Model W gauge boson, gaWW, around 10−4 GeV−1, testing a previously unexplored region of parameter space. Other new particle models that lead to the same experimental signature, including ALPs coupled to gluons or photons, U(1)B gauge bosons, up-philic scalars, and a Type-I two-Higgs doublet model, are also considered for interpretation, and new constraints on previously viable parameter space are presented in this paper.

Exact bifurcation analysis of the static response of a Fermi–Pasta–Ulam softening chain with short and long-range interactions

This paper is devoted to the static bifurcation of a nonlinear elastic chain with softening and both direct and indirect interactions. This system is also known as a generalized softening FPU system (Fermi–Pasta–lam nonlinear lattice) with p=2 nonlinear interactions (nonlinear direct and second-neighbouring interactions). The static response of this n-degree-of-freedom nonlinear system under pure tension loading is theoretically and numerically investigated. The mathematical problem is equivalent to a nonlinear fourth-order difference eigenvalue problem. The bifurcation parameters are calculated from the exact resolution of the fourth-order linearized difference eigenvalue problem. It is shown that the bifurcation diagram of the generalized softening FPU system depends on the stiffness ratio of both the linear and the nonlinear parts of the nonlinear lattice, which accounts for both short range and long range interactions. This system possesses both a saddle node bifurcation (limit point) and some unstable bifurcation branches for the parameters of interest. We show that for some range of structural parameters, the bifurcations in (n−1) unstable bifurcation branches prevail before the limit point. In the complementary domain of the structural parameters, the bifurcations in (n−1) unstable bifurcation branches prevail after the limit point, which means that the system becomes unstable first, at the limit point. At the border between both domains in the space of structural parameters, the bifurcation in (n−1) unstable bifurcation branches coincide with the limit point, with an addition unstable fundamental branch. This case is the hill-top bifurcation, already analysed by Challamel et al. (Int J Non-Linear Mech 156(104509): 1-11, 2023) in the case p=1 interaction. We also numerically highlight the possibility for such a generalized FPU system to possess possible imperfection sensitivity. Numerical results support the fact that the structural boundary of the hill-top bifurcation coincides with the transition between imperfection sensitive to imperfection insensitive systems.

Planetesimal formation in a pressure bump induced by infall

Infall of interstellar material is a potential non-planetary origin of pressure bumps in protoplanetary disks. While pressure bumps arising from other mechanisms have been numerically demonstrated to promote planet formation, the impact of infall-induced pressure bumps remains unexplored. We aim to investigate the potential for planetesimal formation in an infall-induced pressure bump, starting with sub-micrometer-sized dust grains, and to identify the conditions most conducive to triggering this process. We developed a numerical model that integrates axisymmetric infall, dust drift, and dust coagulation, along with planetesimal formation via streaming instability. Our parameter space includes gas viscosity, dust fragmentation velocity, initial disk mass, characteristic disk radius, infall rate and duration, as well as the location and width of the infall region. An infall-induced pressure bump can trap dust from both the infalling material and the outer disk, promoting dust growth. The locally enhanced dust-to-gas ratio triggers streaming instability, forming a planetesimal belt inside the central infall location until the pressure bump is smoothed out by viscous gas diffusion. Planetesimal formation is favored by a massive, narrow streamer infalling onto a low-viscosity, low-mass, and spatially extended disk containing dust with a high fragmentation velocity. This configuration enhances the outward drift speed of dust on the inner side of the pressure bump, while also ensuring the prolonged persistence of the pressure bump. Planetesimal formation can occur even if the infalling material consists solely of gas. A pressure bump induced by infall is a favorable site for dust growth and planetesimal formation, and this mechanism does not require a preexisting massive planet to create the bump.

Susy breaking soft terms in the supersymmetric Pati-Salam landscape from intersecting D6-branes

We investigate the supersymmetry breaking soft terms for all the viable models in the complete landscape of three-family supersymmetric Pati-Salam models arising from intersecting D6-branes on a \U0001d54b6/(ℤ2 × ℤ2) orientifold in type IIA string theory. The calculations are performed in the general scenario of u-moduli dominance with the s-moduli turned on, where the soft terms remain independent of the Yukawa couplings and the Wilson lines. The results for the trilinear coupling, gaugino-masses, squared-mass parameters of squarks, sleptons and Higgs depend on the brane wrapping numbers and the susy breaking parameters. We find that unlike the Yukawa couplings which remain unchanged for the models dual under the exchange of two SU(2) sectors, the corresponding soft term parameters only match for the trilinear coupling and the mass of the gluino. This can be explained by the internal geometry where the Yukawa interactions depend only on the triangular areas of the worldsheet instantons while the soft terms have an additional dependence on the orientation-angles of D6-branes in the three two-tori. In the special limit of parameter space we find universal masses for the Higgs and the gauginos.

Nitrogen Dioxide Detection with Ambipolar Silicon Nanowire Transistor Sensors.

Si nanowire transistors are ideal for the sensitive detection of atmospheric species due to their enhanced sensitivity to changes in the electrostatic potential at the channel surface. In this study, we present unique ambipolar Si junctionless nanowire transistors (Si-JNTs) that incorporate both n- and p-type conduction within a single device. These transistors enable scalable detection of nitrogen dioxide (NO2), a critical atmospheric oxidative pollutant, across a broad concentration range, from high levels (25-50 ppm) to low levels (250 ppb-2 ppm). Acting as an electron acceptor, NO2 generates holes and functions as a pseudodopant for Si-JNTs, altering the conductance and other device parameters. Consequently, ambipolar Si-JNTs exhibit a dual response at room temperature, reacting on both p- and n-conduction channels when exposed to gaseous NO2, thereby offering a larger parameter space compared to a unipolar device. Key characteristics of the Si-JNTs, including on-current (Ion), threshold voltage (Vth) and mobility (μ), were observed to dynamically change on both the p- and n-channels when exposed to NO2. The p-conduction channel showed superior performance across all parameters when compared to the device's n-channel. For example, within the NO2 concentration range of 250 ppb to 2 ppm, the p-channel achieved a responsivity of 37%, significantly surpassing the n-channel's 12.5%. Additionally, the simultaneous evolution of multiple parameters in this dual response space enhances the selectivity of Si-JNTs toward NO2 and improves their ability to distinguish between different pollutant gases, such as NO2, ammonia, sulfur dioxide and methane.

GJ 2126 b: A highly eccentric Jovian exoplanet

We report the discovery of GJ,2126,b a highly eccentric (e = 0.85) Jupiter-like planet orbiting its host star every $272.7$ days. The planet was detected and characterized using $112$ radial velocity (RV) measurements from HARPS (High Accuracy Radial velocity Planet Searcher), provided by HARPS-RVBank. This planet orbits a low-mass star and ranks among the most eccentric exoplanets discovered, placing it in a unique region of the parameter space of the known exoplanet population. This makes it a valuable addition to the exoplanet demographics, helping to refine our understanding of planetary formation and evolution theories.