Bifunctional Research Articles

From deterministic to stochastic: limits of extracting bifurcation diagrams for noisy bistable oscillators with the control-based continuation method

AbstractNoise limits the information that can be experimentally extracted from dynamical systems. In this study, we review the Control-based Continuation (CBC) approach, which is commonly used for experimental characterisation of nonlinear systems with coexisting stable and unstable steady states. The CBC technique, however, uses a deterministic framework, whereas in practice, almost all measurements are subject to some level of random perturbation, and the underlying dynamical system is inherently noisy. In order to discover what the CBC is capable of extracting from inherently noisy experiments, we study the Hopf normal form with quintic terms with additive noise. The bifurcation diagram of the deterministic core of this system is well-known, therefore the discrepancies introduced by noise can be easily assessed. First, we utilise the Step-Matrix Multiplication based Path Integral (SMM-PI) method to approximate the system’s steady state probability density function (PDF) for different intensity noise perturbations. We associate the local extrema of the resulting PDFs with limit cycles, and compare the resulting bifurcation diagram to those captured by CBC. We show that CBC estimates the bifurcation diagram of the noisy system well for noise intensities varying from small to moderate, and in practice, the amplitudes provided by CBC may be accepted as a ’best guess’ proxy for the vibration amplitudes characteristic to the near periodic solutions in a wide range of experiments.

Non-Gaussian tails without stochastic inflation

We show, both analytically andnumerically,thatnon-Gaussian tails in the probability density function of curvature perturbations arise in ultra-slow-roll inflation from the δN formalism, without invoking stochastic inflation. Previously reported discrepancies between both approaches are a consequence of not correctly accounting for momentum perturbations. Once they are taken into account, both approaches agree to an excellent degree. The shape of the tail depends strongly on the phase space of inflation.

Spin-2 Green’s functions on Kerr in radiation gauge

Abstract We construct retarded and advanced Green’s functions for gravitational perturbations in Kerr in an ingoing radiation gauge. Our Green’s functions have a frequency domain piece that has previously been obtained by Ori (2003 Phys. Rev. D 67) based on the Chrzanowski-Cohen-Kegeles metric reconstruction method. As is well known, this piece by itself is not sufficient to obtain an actual Green’s function. We show how to complete it with a piece based on a method by Green et al (2020 Class. Quantum Grav. 37). The completion piece has a completely explicit form in the time-domain and is supported on pairs of points on the same outgoing principal null geodesic which are in the appropriate causal order. We expect our Green’s functions to be useful for gravitational self-force calculations and other perturbation problems on Kerr spacetime.

Bifunctional Nitrogen-Rich Heterocyclic Compounds: Synthesis, Photoluminescence and Energetic Properties.

Nitrogen-rich heterocyclic frameworks have attracted enormous interest in organic chemistry and materials science. However, their potential for developing photoluminescent materials remains underexplored due to their relatively low molecular stabilities. In this work, two tricyclic fused nitrogen-rich fluorescent heterocycles were synthesized and characterized. The photophysical properties of the synthesized 4 and 5 were investigated through theoretical and experimental studies. In addition, their physicochemical and energetic properties and the performance as an additive to the perovskite absorption layer of the perovskite solar cell were also studied.

Revealing the True Cost of Locally Differentially Private Protocols: An Auditing Perspective

While the existing literature on Differential Privacy (DP) auditing predominantly focuses on the centralized model (e.g., in auditing the DP-SGD algorithm), we advocate for extending this approach to audit Local DP (LDP). To achieve this, we introduce the LDP-Auditor framework for empirically estimating the privacy loss of locally differentially private mechanisms. This approach leverages recent advances in designing privacy attacks against LDP frequency estimation protocols. More precisely, through the analysis of numerous state-of-the-art LDP protocols, we extensively explore the factors influencing the privacy audit, such as the impact of different encoding and perturbation functions. Additionally, we investigate the influence of the domain size and the theoretical privacy loss parameters ϵ and δ on local privacy estimation. In-depth case studies are also conducted to explore specific aspects of LDP auditing, including distinguishability attacks on LDP protocols for longitudinal studies and multidimensional data. Finally, we present a notable achievement of our LDP-Auditor framework, which is the discovery of a bug in a state-of-the-art LDP Python package. Overall, our LDP-Auditor framework as well as our study offer valuable insights into the sources of randomness and information loss in LDP protocols. These contributions collectively provide a realistic understanding of the local privacy loss, which can help practitioners in selecting the LDP mechanism and privacy parameters that best align with their specific requirements. We open-sourced LDP-Auditor in [4].

Perturbational duality in optimization under evenly convex assumptions

In this paper, we consider an optimization problem which is embedded into a family of perturbed problems. We associate with it the classical conjugate dual problem and a surrogate dual problem called quasi-dual. For these two pairs of primal–dual problems, we provide necessary and sufficient conditions for zero duality gap, strong duality and converse duality, under evenly convex assumptions involving appropriate sets associated to the data perturbation function. To this aim, we firstly establish some new results for evenly convex and evenly quasiconvex functions. We conclude by applying our results to two remarkable instances of optimization problems.

Cell death and DNA damage via ROS mechanisms after applied antibiotics and antioxidants doses in prostate hyperplasia primary cell cultures.

Tumor heterogeneity results in aggressive cancer phenotypes with acquired resistance. However, combining chemical treatment with adjuvant therapies that cause cellular structure and function perturbations may diminish the ability of cancer cells to resist at chemical treatment and lead to a less aggressive cancer phenotype. Applied treatments on prostate hyperplasia primary cell cultures exerted their antitumor activities through mechanisms including cell cycle blockage, oxidative stress, and cell death induction by flow cytometry methods. A 5.37 mM Chloramphenicol dose acts on prostate hyperplasia cells by increasing the pro-oxidant status, inducing apoptosis, autophagy, and DNA damage, but without ROS changes. Adding 6.30 mM vitamin C or 622 µM vitamin E as a supplement to 859.33 µM Chloramphenicol dose in prostate hyperplasia cells determines a significant increase of ROS level for a part of cells. However, other cells remain refractory to initial ROS, with significant changes in apoptosis, autophagy, and cell cycle arrest in G0/G1 or G2/M. When the dose of Chloramphenicol was increased to 5.37 mM for 6.30 mM of vitamin C, prostate hyperplasia cells reacted by ROS level drastically decreased, cell cycle arrest in G2/M, active apoptosis, and autophagy. The pro-oxidant action of 1.51 mM Erythromycin dose in prostate hyperplasia cell cultures induces changes in the apoptosis mechanisms and cell cycle arrest in G0/G1. Addition of 6.30 mM vitamin C to 1.51 mM Erythromycin dose in hyperplasia cell cultures, the pro-oxidant status determines diminished caspase 3/7 mechanism activation, but ROS level presents similar changes as Chloramphenicol dose and cell cycle arrest in G2/M. Flow cytometric analysis of cell death, oxidative stress, and cell cycle are recommended as laboratory techniques in therapeutic and diagnostic fields.

Set Restabilization of Perturbed Boolean Control Networks

This paper develops a parameter tuning method for solving the set restabilization problem of perturbed Boolean control networks (BCNs). First, the absorbable attractor, which we previously proposed, is recalled. Based on the relationship between attractors, a necessary and sufficient restabilizability criterion is derived. This criterion is used to check whether a perturbed BCN can be stabilized to the original target set by modifying the least number of parameters to the old controller. Furthermore, a constructive method for fine-tuning the old controller is provided if the criterion condition derived above is satisfied. Compared with the existing relevant results, ours have clear advantages, since they can address the set restabilization problem of BCNs subject to multi-column function perturbations, which has not been solved yet. Finally, two examples are employed to show the effectiveness and advantages of our results.

Perturbation approaches to achieving diverse and competitive designs in topology optimisation

Utilising topology optimisation to generate diverse and competitive structures enables designers to create elegant and efficient designs according to their aesthetic intuition and functional needs. This study proposes load and support perturbation approaches based on the bi-directional evolutionary structural optimisation (BESO) method to achieve diverse designs. During the optimisation process, noise is introduced to the sensitivity calculations by randomly perturbing the load angles or material properties near the supports, leading to a variety of local optima. Numerical results demonstrate that the proposed approaches are capable of creating designs with similar stiffness but distinct geometries. In addition, the diversity of the obtained solutions can be controlled by utilising different perturbation functions. This work is of significant practical importance in both architecture and engineering, where multiple design options of high structural performance are in demand.

Towards testing the general bounce cosmology with the CMB B-mode auto-bispectrum

It has been shown that a three-point correlation function of tensor perturbations from a bounce model in general relativity with a minimally-coupled scalar field is highly suppressed, and the resultant three-point function of cosmic microwave background (CMB) B-mode polarizations is too small to be detected by CMB experiments. On the other hand, bounce models in a more general class with a non-minimal derivative coupling between a scalar field and gravity can predict the three-point correlation function of the tensor perturbations without any suppression, the amplitude of which is allowed to be much larger than that in general relativity. In this paper, we evaluate the three-point function of the B-mode polarizations from the general bounce cosmology with the non-minimal coupling and show that a signal-to-noise ratio of the B-mode auto-bispectrum in the general class can reach unity for ℓ max=100 in the full-sky case, with and without the lensing B-mode added to cosmic variance. Considering additionally the LiteBIRD experimental noise, we obtain a SNR smaller than unity.

Roles of boundary and equation-of-motion terms in cosmological correlation functions

We revisit the properties of total time-derivative terms as well as terms proportional to the free equation of motion (EOM) in a Schwinger-Keldysh formalism. They are relevant to the correct calculation of correlation functions of curvature perturbations in the context of inflationary Universe. We show that these two contributions to the action play different roles in the operator or the path-integral formalism, but they give the same correlation functions as each other. As a concrete example, we confirm that the Maldacena's consistency relations for the three-point correlation function in the slow-roll inflationary scenario driven by a minimally coupled canonical scalar field hold in both the operator and path-integral formalisms. We also give some comments on loop calculations.

Cosmic inflation from fluctuating baby-Skyrme brane

In this work, we explore the inflationary dynamics induced by small fluctuations on the Skyrme brane, characterized by a time-dependent perturbative function ϕ̃. In the low-energy regime, the model successfully reproduces standard inflation, with a potential term dictated by the Skyrmion at the brane. Gravity localization is achieved at the brane, and the lowest energy scale is established at the asymptotic boundary. The model demonstrates the capability to emulate standard inflation dynamics, resembling ϕ̃4 potential characteristics under certain conditions. At higher energy regions, the behaviour of ϕ̃ is contingent upon the Skyrme term coupling constant λ, influencing reheating phases. The wave-like nature of fluctuations allows for energy transfer, resulting in a possibly lower reheating temperature. We also discuss the prospect of λ changing sign during inflation, presenting a non-standard coupling dependent on the matter field.

Benchmarking Methods for PROTAC Ternary Complex Structure Prediction.

Proteolysis targeting chimeras (PROTACs) are bifunctional compounds that recruit an E3 ligase to a target protein to induce ubiquitination and degradation of the target. Rational optimization of PROTAC requires a structural model of the ternary complex. In the absence of an experimental structure, computational tools have emerged that attempt to predict PROTAC ternary complexes. Here, we systematically benchmark three commonly used tools: PRosettaC, MOE, and ICM. We find that these PROTAC-focused methods produce an array of ternary complex structures, including some that are observed experimentally, but also many that significantly deviate from the crystal structure. Molecular dynamics simulations show that PROTAC complexes may exist in a multiplicity of configurational states and question the use of experimentally observed structures as a reference for accurate predictions. The pioneering computational tools benchmarked here highlight the promises and challenges in the field and may be more valuable when guided by clear structural and biophysical data. The benchmarking data set that we provide may also be valuable for evaluating other and future computational tools for ternary complex modeling.

Optogenetics in Pancreatic Islets: Actuators and Effects.

The Islets of Langerhans reside within the endocrine pancreas as highly vascularised micro-organs that are responsible for the secretion of key hormones, such as insulin and glucagon. Islet function relies on a range of dynamic molecular processes that include calcium (Ca2+) waves, hormone pulses, and complex interactions between islet cell types. Dysfunction of these processes results in poor maintenance of blood glucose homeostasis and is a hallmark of diabetes. Very recently, the development of optogenetic methods that rely on light-sensitive molecular actuators has allowed perturbing islet function with near physiological spatio-temporal acuity. These actuators harness natural photoreceptor proteins and their engineered variants to manipulate mouse and human cells that are not normally light-responsive. Until recently, optogenetics in islet biology has primarily focused on hormone production and secretion; however, studies on further aspects of islet function, including paracrine regulation between islet cell types and dynamics within intracellular signaling pathways are emerging. Here, we discuss the applicability of optogenetics to islets cells and comprehensively review seminal as well as recent work on optogenetic actuators and their effects in islet function and diabetes mellitus (DM).

A New Application for Cenicriviroc, a Dual CCR2/CCR5 Antagonist, in the Treatment of Painful Diabetic Neuropathy in a Mouse Model.

The ligands of chemokine receptors 2 and 5 (CCR2 and CCR5, respectively) are associated with the pathomechanism of neuropathic pain development, but their role in painful diabetic neuropathy remains unclear. Therefore, the aim of our study was to examine the function of these factors in the hypersensitivity accompanying diabetes. Additionally, we analyzed the analgesic effect of cenicriviroc (CVC), a dual CCR2/CCR5 antagonist, and its influence on the effectiveness of morphine. An increasing number of experimental studies have shown that targeting more than one molecular target is advantageous compared with the coadministration of individual pharmacophores in terms of their analgesic effect. The advantage of using bifunctional compounds is that they gain simultaneous access to two receptors at the same dose, positively affecting their pharmacokinetics and pharmacodynamics and consequently leading to improved analgesia. Experiments were performed on male and female Swiss albino mice with a streptozotocin (STZ, 200 mg/kg, i.p.) model of diabetic neuropathy. We found that the blood glucose level increased, and the mechanical and thermal hypersensitivity developed on the 7th day after STZ administration. In male mice, we observed increased mRNA levels of Ccl2, Ccl5, and Ccl7, while in female mice, we observed additional increases in Ccl8 and Ccl12 levels. We have demonstrated for the first time that a single administration of cenicriviroc relieves pain to a similar extent in male and female mice. Moreover, repeated coadministration of cenicriviroc with morphine delays the development of opioid tolerance, while the best and longest-lasting analgesic effect is achieved by repeated administration of cenicriviroc alone, which reduces pain hypersensitivity in STZ-exposed mice, and unlike morphine, no tolerance to the analgesic effects of CVC is observed until Day 15 of treatment. Based on these results, we suggest that targeting CCR2 and CCR5 with CVC is a potent therapeutic option for novel pain treatments in diabetic neuropathy patients.

Universal distances for extended persistence

The extended persistence diagram is an invariant of piecewise linear functions, which is known to be stable under perturbations of functions with respect to the bottleneck distance as introduced by Cohen–Steiner, Edelsbrunner, and Harer. We address the question of universality, which asks for the largest possible stable distance on extended persistence diagrams, showing that a more discriminative variant of the bottleneck distance is universal. Our result applies more generally to settings where persistence diagrams are considered only up to a certain degree. We achieve our results by establishing a functorial construction and several characteristic properties of relative interlevel set homology, which mirror the classical Eilenberg–Steenrod axioms. Finally, we contrast the bottleneck distance with the interleaving distance of sheaves on the real line by showing that the latter is not intrinsic, let alone universal. This particular result has the further implication that the interleaving distance of Reeb graphs is not intrinsic either.

The Mesoamerican giant toad (<em>Rhinella horribilis</em>) as bioindicator of vegetation degradation in a tropical forest

Identifying species that can serve as bioindicators of environmental quality is essential for monitoring the anthropogenic impact. Common and widespread species can be ideal bioindicators due to their abundance and easy monitoring, but a confirmation of their differential responses as a function of habitat perturbation is needed. Because amphibians are known as good bioindicators of environmental perturbation, we conducted this work to identify whether a common, generalist amphibian species, the Mesoamerican giant toad (Rhinella horribilis), could serve as a bioindicator of environmental degradation in a tropical forest. We sampled toads in two areas of tropical forest that differed in anthropogenic degradation (primary vs. secondary forest), establishing in each of these areas two sections of the same surface area but differing in substrate (grass vs. sand). We analyzed toad abundance, sex ratio, body length and condition, and the amount and distribution across the body of ectoparasites (ticks). We analyzed 59 toads that were infested with 503 ticks. Based on a multi-model inference approach, the results suggested that toads were more abundant and had lower body condition in the secondary than in the primary forest. In the secondary forest, females were proportionally less abundant than males. The tick loads responded to an interaction of the body area with either the forest type or the substrate, with increased occurrence of ticks in toads from secondary forests and from grass sections. The differences found between the primary and secondary forests in sex ratio, toad abundance, body condition, and tick load across body regions are consistent with previous studies in other less common species of amphibians and thus posit R. horribilis as a good bioindicator of anthropic disturbance in this tropical forest.

On the Asymptotic Behavior of the Secular Perturbation Function in the Circular Restricted Three-Body Problem

On the Asymptotic Behavior of the Secular Perturbation Function in the Circular Restricted Three-Body Problem

MODELING THE DYNAMICS OF DEFORMABLE OBJECTS BASED ON VOLUMETRIC PATCHES OF FREE FORMS

A method for solving nonlinear implicit numerical integration problems based on volumetric patches of free forms for modeling deformable objects with high-speed dynamics is proposed. This method improves the accuracy, consistency and controllability of deformation modeling and animation. The method is characterized by speed, accuracy, stability and uses optimization with region decomposition. The method is well suited for modeling deformable bodies with a large time step, in a wide range of deformation dynamics. We propose decomposed optimization, an optimization method based on free-form patches with region decomposition to minimize incremental potentials at each time step. The method uses quadratic matrix decomposition to combine non-overlapping subregions. The Hessian is evaluated once at the beginning of the time step. The advantages of the method are as follows. Geometric primitives and their mathematical models are proposed, which allow the reasonable application of these primitives to solve problems of volume-oriented modeling. Such requirements are met by volumetric patches of free forms based on analytical perturbation functions relative to the base triangles. The decomposed Hessian is constructed for each subregion and calculated using a set of vertices taken from a complete non-decomposed grid. The weights add the missing second-order Hessian data to the vertices of the subregions from the neighbors along the decomposition boundaries. Thanks to this, the descent is performed along the grid coordinates. There is no need to add gradients. During the descent, the gradient is determined. The Hessians under the region are calculated and factorized in parallel once per time step. They are used as an initializer at each iteration. Then the results are mixed together. This ensures stable and continuous high-quality modeling. An automated and reliable optimization method adapted for modeling nonlinear materials, high-speed dynamics and large deformations is proposed.

Gluonic contributions to semi-inclusive DIS in the target fragmentation region

We study one-loop contributions to semi-inclusive deep inelastic scattering in the target fragmentation region for a polarized lepton beam and nucleon target. Complete one-loop results at leading twist are derived, with a particular focus on the gluonic channel. It shows that four structure functions are generated uniquely by the gluon fracture functions starting at one-loop. Additionally, we obtain two structure functions associated with the longitudinal polarization of the virtual photon, and they are contributed by both gluon and quark channels. By combining existing twist-3 results, all eighteen structure functions for the studied process are predicted in terms of fracture functions convoluted with perturbative coefficient functions.