This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian processes and deep neural networks. For nonlinear systems, stability conditions involve inequalities over an infinite number of states in a state space. Sampling-based approaches can simplify these hard conditions into inequalities discretized over a finite number of states. However, this simplification requires margins to compensate for discretization residuals. Large margins degrade the accuracy of stability evaluation, and obtaining appropriate margins for various systems is challenging. This study addresses this challenge by deriving second-order margins for various nonlinear systems containing data-driven models. Because the size of the derived margins decrease quadratically as the discretization interval decreases, the stability evaluation is more accurate than with first-order margins. Furthermore, this study designs feedback controllers by integrating the sampling-based approach with an optimization problem. As a result, the controllers can guarantee stability while simultaneously considering control performance.

Water-content changes in the upper few centimeters control the evaporation response, but this layer is difficult to measure at millimeter-scale spacing. We evaluated a printed-circuit-board-based multi-TDR probe (MTP) in a homogeneous sand column. The probe has eight three-wire measurement sections at depths of 0.28–2.52 cm. Electric-field simulation showed that the response of each section was localized around the embedded conductors, so the measured permittivity had to be treated as a probe-specific response. Calibration against gravimetrically determined water content confirmed that the εMTP–θ relationship differed from the standard Topp equation and required section-specific calibration. The calibrated MTP estimates agreed with the gravimetric reference values, with R2 = 0.996 and root mean square error (RMSE) = 0.0075 m3 m−3. During evaporation, MTP-derived profiles in the upper 0–30 mm were compared with HYDRUS-1D simulations constrained by pressure-head, mass-loss, and water-retention data. The MTP–HYDRUS comparison gave a pooled RMSE of 0.0376 m3 m−3 and a weighted mean absolute error (MAE) of 0.0282 m3 m−3, with the largest differences in the upper 0–20 mm. The results indicate that the MTP can provide independent millimeter-scale water-content profiles for checking near-surface water redistribution and for identifying depths where simulated surface-layer θ profiles depart from direct observations.

Non-canonical disulfide bonds are a hallmark of the VHH domain of heavy-chain antibodies, with predominant bonds between CDRs 1 and 3 and between framework FR2 and CDR3. The former interloop disulfide bond is advantageous for stability and antigen-binding affinity, albeit not indispensable. Importantly, mutations in the cysteine of the interloop disulfide bond of CDRs 1 and 3 can sometimes preserve antigen-binding activity. In contrast, the functional role of the interloop disulfide bond between FR2 and CDR3 remains largely understudied. In this study, we investigated the replacement of the disulfide bond between FR2 and CDR3 with cysteine mutations in aliphatic amino acids (alanine, valine, and isoleucine). These results indicate that this interloop disulfide bond contributes to the structural stabilization of VHH but is not required for antigen binding, consistent with the findings for the disulfide bond between CDRs 1 and 3. Furthermore, the disulfide bond between FR2 and CDR3 was not critical for maintaining reversibility following heat-induced unfolding. Given the prevalence of FR2-CDR3 interloop disulfide bonds in VHHs from llamas and alpacas, these findings provide valuable insights into VHH engineering and applications.

Conventional stochastic control methods have several limitations. They focus on optimizing the average performance and, in some cases, performance variability; however, their problem settings still require an explicit specification of the probability distributions that determine the system's stochastic behavior. Distributionally robust control (DRC) methods have recently been developed to address these challenges. However, many DRC approaches involve handling infinitely many inequalities. For instance, DRC problems based on the Wasserstein distance are commonly obtained by solving semi-infinite programming (SIP) problems. Our proposed method eliminates the need for SIP when solving discrete-time, discounted, distributionally robust optimal control problems. By introducing a penalty term based on a specific distributional distance, we establish upper bounds, and under appropriate conditions, demonstrate the equivalence between distributionally robust optimization problems and mean-variance minimization problems. This reformulation reduces the original DRC problem to a discounted mean-variance cost optimization problem. In linear-quadratic regulator settings, the corresponding control laws are obtained by solving the Riccati equation. Numerical experiments demonstrate that the theoretical maximum value of the discounted cumulative cost for the proposed method is lower than that for the conventional method.

This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties in optimal control. Firstly, the time-invariant stochastic nature violates the principle of optimality and Hamilton-Jacobi equations, which are fundamental tools for solving optimal control problems. Secondly, nonlinear systems must be robustly stabilized against these stochastic parameters. To overcome these difficulties simultaneously, this study presents a parametric-gradient-based method with a penalty function. A controller and cost function are parameterized using basis functions, and a gradient method is employed to optimize the controller by minimizing the parameterized cost function. Crucial challenges in this approach are parameterizing the cost function appropriately and deriving the gradient of the cost. This study provides explicit formulations of an optimally parameterized cost and its gradient. Furthermore, a suitable penalty function is proposed to ensure robust stability, even when using the gradient method. Consequently, the gradient method produces a suboptimal feedback controller that guarantees the robust stability. The effectiveness of the proposed method is demonstrated through numerical simulations, highlighting its performance in comparison with other baseline methods.

Somatic mutations and antibody clone selection occur in B-cell hyper-evolution over extremely brief periods of time. Herein, we developed a technique for antibody screening by immunizing alpacas with antigens and observing antibody sequence transitions over time, a method we named Tracking the Evolution of Antibodies over time. This technique allows the observation of sequence transitions of somatic mutations in antibody populations originating from the same genome. The accumulation of somatic mutations was significantly associated with enhanced antigen-binding capacity and reduced stability in clusters. In comparison with the first clone to emerge in this cluster, numerous clones exhibited a decline in thermal stability, with a maximum variation of 21°C. Somatic mutations within the clusters demonstrating high similarity were observed to be concentrated in CDR-1, CDR-2, and FR-3. This suggests that these mutations have a significant impact on binding capacity and stability. However, the correlation between antigen binding capacity and stability was insignificant and weak. The thermal stability of antibodies correlated with acid and alkali resistance, with clones exhibiting lower thermal stability demonstrating higher acid and alkali resistance in antigen-antibody complexes. The results indicate that in the antibody selection process, the strength of antigen binding involves optimizing stability, with antibodies with more flexible structures being selected.

Antibody-drug conjugates (ADCs) that equip multiple cytotoxic drugs on an antibody have been developed, particularly in cancer chemotherapy. In the treatment of viral infectious diseases, there are dominantly fewer examples of ADCs. Recently, we developed double-warhead ADCs targeting the entry of human immunodeficiency virus type 1 (HIV-1) into host cells. One is a small molecule CD4 mimic, which is a competitive inhibitor against the interaction between a viral envelop protein, gp120, and a primary receptor, CD4, and the other is neutralizing antibodies, which recognize the regions of gp120, exposed by its conformational change after the interaction between gp120 and CD4. The conformational changes are also triggered by the binding of gp120 and a CD4 mimic, and therefore, the ADCs show positive effects on anti-HIV-1 activity compared to the combinational use of CD4 mimics with neutralizing antibodies. Herein, we synthesized novel ADCs containing a CD4 mimic and a neutralizing antibody, KD-247, using tCAP chemistry, which is based on a site-specific modification method for IgG antibodies, and evaluated their anti-HIV-1 and antibody-dependent cellular cytotoxicity (ADCC) activities. As a result, the KD-247-adopted ADCs demonstrated enhanced anti-HIV-1 activities, whereas all of the ADCs reduced their ADCC activities.

In this article, we experimentally and theoretically analyze practical consensus stimulated by a small number of committed players who stubbornly promote an alternative in a binary-choice quiz with graded confidence. Our study bridges the gap between theory and experiment on practical consensus, since prior work on practical consensus is limited to theoretical analyses. In practical consensus, socially chosen opinions converge to a bounded interval, while admitting some deviations from exact consensus. We formulate a novel heterogeneous population dynamics model that represents the diversity of boundedly rational decision-makers to capture practical consensus in an on-site multiround group experiment. From a theoretical analysis, we prove that practical consensus is shaped by the heterogeneity of boundedly rational decision-makers. Our findings contribute to a better understanding of practical consensus and may provide insights into the spread of new alternatives in binary-choice settings with graded confidence.

Monoclonal antibodies are indispensable therapeutic agents for various diseases, including cancer, autoimmune disorders, and infectious diseases. Glycoprotein A33 (GPA33), a cell surface antigen highly expressed in colorectal cancer, provides a compelling therapeutic target; however, the species-specificity of anti-GPA33 antibodies has limited their utility in preclinical models, thus inhibiting their development. Here, we generated and characterized fully human, cross-reactive anti-GPA33 antibodies using phage-display technology with transchromosomic antibody-producing animals. The resulting single-chain variable fragment and single-chain variable fragment crystallizable antibodies exhibited high specificity and affinity for both human and mouse GPA33. In vivo imaging confirmed their targeted retention in mouse intestine, indicating their potential for developing targeted therapeutic approaches. The ability of these antibodies to recognize both human and murine GPA33 enhances their applicability in preclinical models, improving their translation from experimental to clinical applications. These results highlight the feasibility of developing cross-reactive, fully human antibodies and support the advancement of GPA33-targeted diagnostic approaches and the exploration of novel therapeutic strategies for relevant gastrointestinal diseases.

This study introduces a novel theoretical framework for analyzing heteroscedastic Gaussian processes (HGPs) that identify unknown systems in a data-driven manner. Although HGPs effectively address the heteroscedasticity of noise in complex training datasets, calculating the exact posterior distributions of the HGPs is challenging, as these distributions are no longer multivariate normal. This study derives the exact means, variances, and cumulative distributions of the posterior distributions. Furthermore, the derived theoretical findings are applied to a chance-constrained tracking controller. After an HGP identifies an unknown disturbance in a plant system, the controller can handle chance constraints regarding the system despite the presence of the disturbance.

Distributionally robust optimal control (DROC) is gaining interest. This study presents a reformulation method for discrete DROC (DDROC) problems to design optimal control policies under a worst-case distributional uncertainty. The reformulation of DDROC problems impacts both the utility of tractable improvements in continuous DROC problems and the inherent discretization modeling of DROC problems. DROC is believed to have tractability issues; namely, infinite inequalities emerge over the distribution space. Therefore, investigating tractable reformulation methods for these DROC problems is crucial. One such method utilizes the strong dualities of the worst-case expectations. However, previous studies demonstrated that certain non-trivial inequalities remain after the reformulation. To enhance the tractability of DDROC, the proposed method reformulates DDROC problems into one-layer smooth convex programming with only a few trivial inequalities. The proposed method is applied to a DDROC version of a patrol-agent design problem.

This paper presents weighted stochastic Riccati (WSR) equations for designing multiple types of optimal controllers for linear stochastic systems. The stochastic system matrices are independent and identically distributed (i.i.d.) to represent uncertainty and noise in the systems. However, it is difficult to design multiple types of controllers for systems with i.i.d. matrices while the stochasticity can invoke unpredictable control results. A critical limitation of such i.i.d. systems is that Riccati-like algebraic equations cannot be applied to complex controller design. To overcome this limitation, the proposed WSR equations employ a weighted expectation of stochastic algebraic equations. The weighted expectation is calculated using a weight function designed to handle statistical properties of the control policy. Solutions to the WSR equations provide multiple policies depending on the weight function, which contain the deterministic optimal, stochastic optimal, and risk-sensitive linear (RSL) control. This study presents two approaches to solve the WSR equations efficiently: calculating WSR difference equations iteratively and employing Newton's method. Moreover, designing the weight function yields a novel controller termed the robust RSL controller that has both a risk-sensitive policy and robustness to randomness occurring in stochastic control design.

This paper presents a new paradigm to stabilize uncertain stochastic linear systems. Herein, second moment polytopic (SMP) systems are proposed that generalize systems with both uncertainty and randomness. The SMP systems are characterized by second moments of the stochastic system matrices and the uncertain parameters. Further, a fundamental theory for guaranteeing stability of the SMP systems is established. It is challenging to analyze the SMP systems owing to both the uncertainty and randomness. An idea to overcome this difficulty is to expand the SMP systems and exclude the randomness. Because the expanded systems contain only the uncertainty, their stability can be analyzed via robust stability theory. The stability of the expanded systems is equivalent to statistical stability of the SMP systems. These facts provide sufficient conditions for the stability of the SMP systems as linear matrix inequalities (MIs). In controller design for the SMP systems, the linear MIs reduce to cubic MIs whose solutions correspond to feedback gains. The cubic MIs are transformed into simpler quadratic MIs that can be solved using optimization techniques. Moreover, solving such non-convex MIs is relaxed into the iteration of a convex optimization. Solutions to the iterative optimization provide feedback gains that stabilize the SMP systems. As demonstrated here, the SMP systems represent linear dynamics with uncertain mean and covariance and other existing systems such as independently identically distributed dynamics and random polytopes. Finally, a numerical simulation shows the effectiveness of the proposed method.

Direct modification of native antibodies with affinity peptides remains a significant challenge, primarily because the affinity peptide often stays bound to the antibody and blocks its interaction with key receptors. In this study, we developed tCAP(N3), a novel traceless chemical conjugation method that employs an affinity peptide. tCAP(N3) can be stored for over a year at refrigerated temperature, as it contains an active ester precursor that can be spontaneously activated under neutral conditions. When tCAP(N3) was mixed with a target native IgG, Ac-Lys(N3)-Gly-Gly was site-selectively transferred onto Lys248, yielding divalently azidated IgG that can be further modified with DBCO compounds. The resulting antibody conjugates retained Fc receptor binding and antigen recognition comparable to the parent IgG.

This study introduces an uncertainty-aware, mesh-free numerical method for solving Kolmogorov PDEs. In the proposed method, we use Gaussian process regression (GPR) to smoothly interpolate pointwise solutions that are obtained by Monte Carlo methods based on the Feynman–Kac formula. The proposed method has two main advantages: 1. uncertainty assessment, which provides numerical information about the validity of the solution, and 2. mesh-free computation, which allows one to choose any low-dimensional bounded domain for reducing the computational cost. The quality of the solution is improved by adjusting the kernel function and incorporating noise information from the Monte Carlo samples into the GPR noise model. The performance of the method is rigorously analyzed based on a theoretical lower bound on the posterior variance, which serves as a measure of the error between the numerical and true solutions. Extensive tests on three representative PDEs demonstrate the high accuracy and robustness of the method compared to existing methods.

Immunoglobulin G (IgG)-binding peptides have been widely used in medicinal chemistry, particularly in the preparation of homogeneous antibody-drug conjugates (ADCs). The dissociation constant (Kd) and kinetic parameters (kon and koff) are critical determinants of peptide performance in such applications. In this study, we conducted a structure-activity relationship (SAR) analysis of the IgG-binding peptide 15-IgBP, focusing on Asp3, Tyr6, and Thr15, to identify more potent derivatives with favorable binding affinities and kinetic profiles. Peptides with appropriately tuned ionic structures exhibited rapid binding and release properties, whereas hydrophobic substitutions in solvent-exposed regions led to slower dissociation. By integrating these SAR findings, we identified the optimized affinity peptides, IAPG-2 and IAPG-3, with sub-nanomolar binding affinities (Kd = 0.753 and 0.705 nM, respectively).

Neural networks capable of approximating complex nonlinearities have found extensive application in data-driven control of nonlinear dynamical systems. However, fast online identification and control of unknown dynamics remain central challenges. This paper integrates echo-state networks (ESNs) – reservoir computing models implemented with recurrent neural networks – and model predictive path integral (MPPI) control – sampling-based variants of model predictive control – to meet these challenges. The proposed reservoir predictive path integral (RPPI) enables fast learning of nonlinear dynamics with ESN and exploits the learned nonlinearities directly in parallelized MPPI control computation without linearization approximations. The framework is further extended to uncertainty-aware RPPI (URPPI), which leverages ESN uncertainty to balance exploration and exploitation: exploratory inputs dominate during early learning, while exploitative inputs prevail as model confidence grows. Experiments on controlling the Duffing oscillator and four-tank systems demonstrate that URPPI improves control performance, reducing control costs by up to 60

In this paper, we analyze a novel continuous-time dynamical binary choice model that unifies several logit dynamics in the presence of a committed minority and internal/external conformity biases. Each logit dynamics represents a population of decision makers in a group (i.e., a subset of society), who choose one from two available strategies. The internal conformity bias is regarded as an inertia which causes people in the group to stick with their own majority. The external conformity bias indicates a social coordination which drives every person in society to the social majority. Based on control theoretic insights, we prove that the committed minority eventually supersedes the majority when every person has an appropriately bounded rationality. Numerical experiments demonstrate the present analytical results.

This letter analyzes the contraction property of the nonlinear systems controlled by suboptimal model predictive control (MPC) using the continuation method. We propose a contraction metric that reflects the hierarchical dynamics inherent in the continuation method. We derive a pair of matrix inequalities that elucidate the impact of suboptimality on the contraction of the optimally controlled closed-loop system. A numerical example is presented to verify our contraction analysis. Our results are applicable to other MPCs than stabilization, including economic MPC.

Phytoplankton growth can cause red tide, lowering water quality and damaging fisheries. The simple Lotka–Volterra model (LV model), estimating the population changes in different species, is often used to analyze the growth and competition of causative species. However, the LV model has not been sufficiently applied to examining the actual occurrence and development of red tides in the field. Therefore, the mechanism of seasonal dominant species replacement and applicability of the LV model were studied to analyze the competition between the harmful raphidophytes Chattonella marina and Heterosigma akashiwo. Sensitivity analysis was performed, and optimization method of competition coefficient (α) was discussed by comparison with measured data from culture experiments. We found that it is crucial to evaluate in advance the initial cell density conditions under which the population size changes concerning α (the order of root mean squared logarithmic error ≥ 10−2). Using this as a reference, we pointed that the initial cell density difference between the two species in co-culture experiments should be as large as possible. In addition, simulation analysis using the model revealed that growth rate (r) and carrying capacity (K) determine H. akashiwo dominance in spring, and the increase in α due to rising temperatures causes C. marina dominance in summer. Comparing α of C. marina with α of C. antiqua cited from a previous study found that the formation of red tides of C. marina less than that of C. antiqua can be explained by α that is 0.42 times smaller than α of C. antiqua. Moreover, the increase in α with increasing temperature is related to the physiological and ecological characteristics of C. marina, which is more likely to dominate the space suitable for growth with temperature rise. We consider that investigations of α, in particular, contributes to modeling various competition and more improving accuracy in analyses. These results provide valuable scientific findings on the occurrence and development of red tide flagellates and their analytical method.