Exact Reduction Research Articles

Construction and Function of Thiolate-Bridged Diiron NxHy Nitrogenase Model Complexes.

ConspectusBiological nitrogen fixation mediated by nitrogenases has garnered significant research interest due to its critical importance to the development of efficient catalysts for mild ammonia synthesis. Although the active center of the most studied FeMo-nitrogenases has been determined to be a complicated [Fe7S9MoC] hetero-multinuclear metal-sulfur cluster known as the FeMo-cofactor, the exact binding site and reduction pathway of N2 remain a subject of debate. Over the past decades, the majority of studies have focused on mononuclear molybdenum or iron centers as potential reaction sites. In stark contrast, cooperative activation of N2 through bi- or multimetallic centers has been largely overlooked and underexplored, despite the renewed interest sparked by recent biochemical and computational studies. Consequently, constructing bioinspired bi- or multinuclear metallic model complexes presents an intriguing yet challenging prospect. In this Account, we detail our long-standing research on the design and synthesis of novel thiolate-bridged diiron complexes as nitrogenase models and their application to chemical simulations of potential biological N2 reduction pathways.Inspired by the structural and electronic features of the potential diiron active center in the belt region of the FeMo-cofactor, we have designed and synthesized a series of new thiolate-bridged diiron nitrogenase model complexes, wherein iron centers with +2 or +3 oxidation states are coordinated by Cp* as carbon-based donors and thiolate ligands as sulfur donors. Through the synergistic interaction between the two iron centers, unstable diazene (NH═NH) species can be trapped to generate the first example of a [Fe2S2]-type complex bearing a cis-μ-η1:η1-NH═NH subunit. Significantly, this species can not only catalyze the reductive N-N bond cleavage of hydrazine to ammonia but also trigger a stepwise reduction sequence NH═NH → [NH2-NH]- → [NH]2-(+NH3) → [NH2]- → NH3. Furthermore, an unprecedented thiolate-bridged diiron μ-nitride featuring a bent Fe-N-Fe moiety was successfully isolated and structurally characterized. Importantly, this diiron μ-nitride can undergo successive proton-coupled electron transfer processes to efficiently release ammonia in the presence of separate protons and electrons and can even be directly hydrogenated using H2 as a combination of protons and electrons for high-yield ammonia formation. Based on combined experimental and computational studies, we proposed two distinct reductive transformation sequences on the diiron centers, which involve a series of crucial NxHy intermediates. Moreover, we also achieved catalytic N2 reduction to silylamines with [Fe2S2]-type complexes by ligand modulation.Our bioinspired diiron cooperative scaffold may provide a suitable model for probing the potential N2 stepwise reduction pathways from the molecular level. Different from the traditional alternating and distal pathways dominated by mononuclear iron or molybdenum complexes, our proposed alternating transformation route based on the diiron centers may not involve the N2H4 intermediate, and the convergence point of the alternating and terminal pathways is imide, not amide. Our research strategy could inform the design and development of new types of bioinspired catalysts for mild and efficient nitrogen reduction in the future.

Dome versus single-cut osteotomies for correction of long bone deformities—technical considerations

Corrective osteotomy allows to improve joint loading, pain and function. In complex deformities, the biggest challenge is to define the optimal surgical solution, while considering anatomical, technical and biomechanical factors. While the single-cut osteotomy (SCOT) and focal dome osteotomy (FDO) are well-established treatment options, their mathematical relationship remain largely unclear. The aim of the study was (1) to describe the close mathematical relationship between the SCOT and FDO and (2) to analyze and introduce a novel technique—the stepped FDO—as a modification of the classic FDO. The mathematical background and relationship of SCOT and FDO are described for the example of a femoral deformity correction and visualized using a 3D surface model taking into account the benefits for the clinical application. The novel modifications of the stepped FDO are introduced and its technical and clinical feasibility demonstrated. Both, SCOT and FDO, rely on the same deformity axis that defines the rotation axis k for a 3D deformity correction. To achieve the desired correction using a SCOT, the resulting cutting plane is perpendicular to k, while using a FDO will result in a cylindrical cut with a central axis parallel to k. The SCOT and FDO demonstrate a strong mathematical relation, as both methods rely on the same deformity axis, however, resulting in different cutting planes. These characteristics enable a complementary use when defining the optimal type of osteotomy. This understanding enables a more versatile planning approach when considering factors as the surgical approach, biomechanical characteristics of fixation or soft tissue conditions. The newly introduced stepped FDO facilitates an exact reduction of the bone fragments and potentially expands the clinical applicability of the FDO.

Decentralized Swarm Control in Communication-Constrained Environments Using a Blended Leader Follower-Artificial Potential Field with Biologically Inspired Interactions

Abstract This paper presents a study of how communication ranges influence the performance of a new decentralized control method for swarms of autonomously navigating ground vehicles that uses a blended leader-follower / artificial potential field approach. While teams of autonomous ground vehicles (AGV) that can navigate autonomously through off-road terrain have a variety of potential uses, it may be difficult to control the team in low-infrastructure environments that lack long-range radio communications capabilities. In this work, we propose a novel decentralized swarm control algorithm that combines the potential-field planning method with the leader-follower control algorithm and biologically-inspired inter-robot interactions to effectively control the navigation of a team of AGV (swarm) through rough terrain using only a single lead vehicle. We use simulated experimentation to demonstrate the robustness of this approach using only point-to-point wireless communication with realistic communication ranges. Furthermore, we analyze the range requirements of the communication network as the number in the swarm increases. We find that wireless communication range must increase as the number of agents in the swarm increases in order to effectively control the swarm. Our analysis showed that mission success decreased by 40% when the communication range was reduced from 100 meters to 200 meters, with the exact reduction also depending on the number of vehicles.

Comparative Analysis of Metal Electrodeposition Rates towards Formation of High-Entropy WFeCoNiCu Alloy.

This study presents a calculation and comparison of Fe, Co, Ni and Cu deposition rates in the tungsten codeposition process based on the electrodeposition of numerous tungsten alloys. Eight different tungsten alloys containing from two to five metals were electrodeposited in constant conditions in order to compare the exact reduction rates. The calculated rates enabled control of the alloy composition precise enough to obtain a high-entropy WFeCoNiCu alloy with a well-balanced composition. The introduction of copper to form the quinternary alloy was found to catalyze the whole process, increasing the deposition rates of all the components of the high-entropy alloy.

Exact hierarchical reductions of dynamical models via linear transformations

Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional model in which each macro-variable can be directly related to the original variables, and it is thus a natural step towards the model’s formal analysis and mechanistic understanding. We present an algorithm which, given a polynomial ODE model, computes a longest possible chain of exact linear reductions of the model such that each reduction refines the previous one, thus giving a user control of the level of detail preserved by the reduction. This significantly generalizes over the existing approaches which compute only the reduction of the lowest dimension subject to an approach-specific constraint. The algorithm reduces finding exact linear reductions to a question about representations of finite-dimensional algebras. We provide an implementation of the algorithm, demonstrate its performance on a set of benchmarks, and illustrate the applicability via case studies. Our implementation is freely available at https://github.com/x3042/ExactODEReduction.jl.

Exact Model Reduction for Discrete-Time Conditional Quantum Dynamics

Exact Model Reduction for Discrete-Time Conditional Quantum Dynamics

Reduction of Metabolic Active Tumor Volume Prior to CAR T-Cell Therapy Improves Survival Outcomes in Patients with Large B-Cell Lymphoma

Introduction CD19-targeted chimeric antigen receptor (CAR) T-cell therapy has become the standard 2 nd or 3 rd line therapy for patients with relapsed or refractory Large B-cell lymphoma (r/r LBCL). As part of this treatment bridging therapy is frequently used between T-cell apheresis and CAR T-cell infusion in order to limit disease progression, diminish lymphoma-related symptoms and/or reduce tumor volume. Bridging therapy has shown to be feasible, safe and effective in patients prior to infusion. In addition, a lower tumor volume is associated with better treatment outcomes and less toxicity. However, the exact reduction and dynamics in metabolic active tumor volume (MATV) are unknown. Here we investigated the relation of changes in pre-apheresis (baseline) MATV, based on 18F-FDG PET scans, and pre-lymphodepleting chemotherapy (pre-LD) MATV with CAR T-cell outcomes and toxicities in patients with r/r LBCL. Methods Baseline and pre-LD MATVs and PET characteristics were calculated semi-automatically of patients who were treated with CAR T-cell therapy. A Standardized Uptake Value (SUV) threshold of 2.5 was used to maintain robustness and avoid MATV underestimation. Bridging strategies consisted of radiotherapy, chemotherapy, or a combination of both. Primary endpoints were duration of response (DOR) and overall survival (OS). Secondary endpoints included cytokine release syndrome (CRS) and immune effector cell-associated neurotoxicity syndrome (ICANS). The Youden index was used to identify the optimal cut-off for dividing patients into low- and high-MATV groups to predict DOR at 2 years. Two-year DOR and OS rates were estimated using Kaplan-Meier curves and the log-rank test was utilized to compare the differences among low- and high-MATV patient groups. Univariable analysis was performed with Cox regression for DOR and OS, and with logistic regression for CRS and ICANS. Results Seventy-four patients with LBCL and treated with CAR T-cell therapy were included in the study. For all patients baseline 18F-FDG PET scans were available, whereof in 68 patients the pre-LD scans. The median baseline MATV was 180 cc (IQR 64 - 426) with a median SUV max of 18.8 (IQR 11.9 - 28.1) and increased to 241 cc (IQR 75 - 525) at pre-LD, with a median SUV max of 21.0 (IQR 12.8 - 31.3). The optimal cut-offs for low- and high-MATV patient groups at baseline and pre-LD were 190 cc and 480 cc, respectively. Patients with a low MATV baseline had a better DOR (Figure 1A) and OS compared to high MATV baseline patients (both p < 0.001). Patients with a high MATV baseline that was reduced to a low MATV pre-LD showed a significant improvement in DOR (Figure 1B) and OS, compared to patients with a high MATV pre-LD ( p = 0.036 for DOR; p = 0.015 for OS). Univariable analysis showed that a high baseline MATV was associated with a worse DOR (HR 6.43 CI [2.15 - 19.20]; p < 0.001) and OS (HR 6.97 CI [2.33 - 20.80]; p < 0.001). A high pre-LD MATV was also associated with a worse DOR (HR 4.86 CI [1.98 - 12.00]; p < 0.001) and OS (HR 5.87 [2.41 - 14.30]; p < 0.001). Other significant associations with DOR and OS were observed for pre-LD lactate dehydrogenase (LDH), the IPI score for DOR exclusively, and gender and bridging therapy for OS exclusively. Conclusions We showed that patients with a low MATV compared to a high MATV at baseline have better survival outcomes and less toxicity. Additionally, reducing tumor volume by applying bridging therapy in patients with a high baseline MATV, results in a significant better DOR and OS. Reducing the MATV before CAR T-cell infusion is therefore essential in CAR T-cell therapy patient care and provides a rationale for the use of more intensive bridging therapies.

Wellposedness for a (1+1)-dimensional wave equation with quasilinear boundary condition

We consider the linear wave equation on with initial conditions and a nonlinear Neumann boundary condition at x = 0. This problem is an exact reduction of a nonlinear Maxwell problem in electrodynamics. In the case where is an increasing homeomorphism we study global existence, uniqueness and wellposedness of the initial value problem by the method of characteristics and fixed point methods. We also prove conservation of energy and momentum and discuss why there is no wellposedness in the case where f is a decreasing homeomorphism. Finally we show that previously known time-periodic, spatially localized solutions (breathers) of the wave equation with the nonlinear Neumann boundary condition at x = 0 have enough regularity to solve the initial value problem with their own initial data.

Reduction of Search Space for the Mean Partition Problem

The contributions of this paper are threefold. First, it conducts a formal comparison of the primary approaches to consensus clustering, using the concepts of agreement and consent. Secondly, it presents theoretical evidence justifying the preference for mean-based methods, which rely on consent, over other agreement-based procedural methods like the q-rule, which are now mostly used as quality evaluators in practice. Thirdly, the paper computes the exact reduction achieved by criteria available in existing literature to assess the quality of mean-based consensus solutions and reduce the search space’s size. Finally, it compiles the regions where consensus functions associated with well-known dissimilarity measures, such as the Mirkin metric and Variation of Information, accumulate their consensus solutions.

Pacing-Induced Cardiomyopathy in Leadless and Traditional Pacemakers: A Single-Center Retrospective Analysis.

Pacing-induced cardiomyopathy (PICM) is a clinical syndrome that is characterized by a drop in the left ventricular ejection fraction (LVEF) due to chronic high-burden right ventricular (RV) pacing. It has been postulated that leadless pacemakers (LPs) cause decreased risk of PICM compared to transvenous pacemakers (TVPs), but the exact risk reduction is unknown. We performed a single-center retrospective analysis of adults who received an LP or TVP between January 1, 2014, and April 1, 2022, and had echocardiograms before and after the pacemaker implant. This study's outcomes were the RV pacing percentage, change in EF, the need for cardiac resynchronization therapy (CRT) upgrade, and follow-up duration. A Wilcoxon rank-sum test calculated the change in EF. RV time, defined as the duration from pacemaker placement to the follow-up echocardiogram in months multiplied by the RV pacing percentage, served as a surrogate for how long the RV was paced. A total of 614 patients were screened, and 198 patients were included in the study, where 72 received LP and 126 received TVP. The median follow-up was 480 days. The average of the reported RV percentage pacing was 63.43% for LP and 71.30% for TVP (p=0.14). The incidence of PICM and CRT upgrade was 44% and 9.7%in the LP group and37% and 9.5%in the TVP group(p=0.3 and p>0.9), respectively. After accounting for age, sex, LP versus TVP, atrioventricular nodal ablation, RV pacing percentage, and follow-up duration, univariate analysis showed that RV time was significantly different between the two types of pacemakers (13.54 ± 14.21 months (LP) versus 9.26 ± 13.95 months (TVP), p=0.009). The difference in RV time between patients who underwent CRT upgrade and those who did not was statistically insignificant (12.11 ± 14.47 months (no CRT) versus 9.19 ± 12.00 months (CRT), p=0.5). This analysis demonstrated that the incidence of PICM was high in both groups (44% (LP) versus 37% (TVP)), despite significantly more RV time in patients with LP. There was no difference in CRT upgrade between LP and TVP.

Analysis of the response of damped and parametrically driven, strongly anharmonic Klein-Gordon chain - Part 2: Beat-waves

This paper continues a series of publications devoted to the analysis of strongly nonlinear wave phenomena, emerging in genuinely anharmonic, Klein-Gordon cyclic chains, subjected to a traveling-wave parametric excitation. In this study, we analyze a special type of nonlinear waves, which will be further referred to as beat-waves. These are spatially extended, and strongly modulated waves manifested by the extreme amplitude modulation, which can be of stationary or nonstationary type. Stationary beat-waves of Klein-Gordon chains propagate with constant group velocity, that depends on the beat-wave amplitude. In the vicinity of 2:1 parametric resonance, we derive the parametrically driven, discrete p-Schrödinger (PD-DpS) model, which depicts the slow modulation of the response of a parametric oscillator chain. Special coordinates' transformation applied on the PD-DpS model allows the exact reduction of extremely modulated beat-waves to an invariant manifold of this slow-flow system. The system dynamics reduced to the beat-wave invariant manifold is depicted by three collective coordinates. In the undamped case, the analysis of the slow-flow system dynamics on the invariant manifold reveals a special family of nonlinear beat-waves characterized by an extreme amplitude modulation. Among these beat-wave solutions lying on the manifold, our analysis identifies some special solutions manifested by the solitary-pulse like, temporal evolution of the beat-wave amplitude which can either decay to zero or to a constant nonzero value. We derive the exact analytical solutions for these special types of waves as well as obtain an explicit analytical approximation for the beat-waves of other types. In the damped case, analysis of the slow-flow system dynamics on the invariant manifold fully recovers the mechanism of system synchronization on the special, stationary beat-wave solutions characterized by the harmonically modulated envelope. Importantly, the derived reduced order model accurately captures the transient evolution stage as well as the steady-state stage of the collective beat-wave response of PD-DpS model, initialized on the beat-wave invariant manifold. A detailed bifurcation analysis of the stationary undamped as well as the stationary damped beat-waves recovers their entire bifurcation structure and enables to fully characterize the zones of system parameters guaranteeing the existence of this special type of non-linear wave solutions. The results of analytical study of various types of beat wave solutions are in excellent agreement with the results of numerical simulation of both PD-DpS as well as the original, parametrically driven, genuinely an-harmonic, discrete Klein-Gordon model.

Internal spillover effect of carbon emission between transportation sectors and electricity generation sectors

The exact carbon reduction potential of transportation electrification has not been answered directly from the coupled view of electric power transmission and transportation. To address this issue, the multi-regional input-output model and quasi-input–output model are used. Through simulation results comparison between the baseline scenario and transportation electrification scenario, we can observe that transportation electrification scenario would finally reduce 403 million tons, while the increase of 302 million tons of CO2 from the electricity generation sector due to the spatial spillover effect offsets the reduced 705 million-tons decarbonization benefits of the traffic transportation sector, as well as the decarbonization benefits of cleaner electricity generation. The total reduced CO2 emissions under the combined scenario are 1997 million tons, which is 94 million tons larger than the overall effect of the separate implementation of transportation electrification scenario and cleaner electricity generation scenario. We conclude that to reduce carbon emission transfer, much greater attention needs to be paid to cleaner generation mix construction.

Cattaneo-Christov double diffusion based heat transport analysis for nanofluid flows induced by a moving plate

Hybrid nanofluids have gained much attention due to their better stability, enhanced thermal conductivity, and physical strength. This manuscript investigates nanofluid flow, induced due to an infinite plate, which is moving (at a constant velocity) toward/receding from normal stagnation point flow. The surface of the plate is suspended and immersed with water as a base fluid and nanoparticles, namely Copper and Alumina. The flow is governed by Reynolds number (Re), which is proportional to the constant velocity of the moving plate and is an exact reduction of the Navier–Stokes equations. Moreover, Hiemenz’s planar and Homann’s axisymmetric flows normal to the stagnation point are considered. Heat transport analysis is carried out by using Cattaneo–Christov theory with Ohmic heating and heat source/sink effects. The governing equations are solved by bvp4c in MATLAB. The behavior of skin friction, flow, and energy distribution is perceived by variation of pertinent parameters. The numerical and asymptotic solutions are computed for the wall shear stress parameter. It is seen that the numerical solution matches its asymptotic behaviors over an intermediate range of small and large valued Reynolds number. The asymptotic values (small-Re) of wall stress reduces for plate advancing toward the stagnation-point flow and receding from the stagnation-point flow for Hiemenz and Homann flow. The increment in magnetic parameter reduced the fluid flow by generating a resistive force against it; however, the energy of the system is enhanced because of it. The augmentation of nanofluid volume fraction initiates the random motion among the nanoparticles which raises the temperature field. Thermal relaxation time parameter causes the particles to require supplementary time for the conduction of heat toward the adjacent particles, which declines the thermal transport. In general, the thermal transport is enhanced for the hybrid nanofluids rather than mono nanofluids.

The optimal configuration of negative stiffness inerter-based base isolators in multi-storey buildings

The negative stiffness inerter-based base isolators (NSIBI) are introduced in this paper. The negative stiffness device and inerters are installed inside the core of the conventional base isolators (CBI) to enhance their dynamic response reduction capacity. The novel isolators have been installed at the multi-storey building’s base to mitigate their dynamic responses during vibration. H2 optimization method applies to derive the exact closed-form expression for negative stiffness inerter-based base isolators’ optimal design parameters, such as frequency and viscous damping ratio for multi-storey buildings. Applying these H2 optimized design parameters, the optimum NSIBI for dynamic response mitigation of multi-storey buildings have been achieved. The dynamic responses of the NSIBI-controlled multi-storey buildings are compared with the dynamic responses of multi-storey buildings isolated by optimum CBI to determine the exact superior dynamic response reduction capacity of optimum NSIBI. The dynamic responses of isolated structures in the frequency domain are evaluated by forming the transfer function. Therefore, for five-storey buildings, the dynamic response reduction capacity of NSIBI is significantly 51.93% and 81.24% superior to the dynamic response reduction capacity of CBI subjected to harmonic and random-white excitations. In contrast, for ten-storey buildings, the optimum NSIBI has 77.73% and 94.02% more dynamic response reduction capacity than the optimum CBI subjected to harmonic and random-white excitations. In addition, using the Newmark beta method, a numerical study further conducts to verify the accuracy of the H2 optimized design parameters by obtaining the time history results for isolated structures subjected to near-field pulse-type earthquake base excitations. Accordingly, the optimum NSIBI have 57.591% and 55.398% more displacement and acceleration capacity than the optimum CBI for five-storey buildings. Besides, for ten-storey buildings, the displacement and acceleration capacities of optimum NSIBI are significantly around 56.42%and 55.80%, superior to the optimum CBI. Thus, the vibration reduction capacity of optimum CBI is significantly decreasing while the storey level of the multi-storey buildings increases, whereas NSIBI is still efficient in reducing the dynamic responses effectively. The paper’s outcomes are mathematically accurate and applicable to practical implementation.

Population spiking and bursting in next-generation neural masses with spike-frequency adaptation.

Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the macroscopic dynamics of excitatory and inhibitory networks of quadratic integrate-and-fire (QIF) neurons coupled via exponentially decaying post-synaptic potentials. In particular, we have studied the population activities by employing an exact mean-field reduction, which gives rise to next-generation neural mass models. This low-dimensional reduction allows for the derivation of bifurcation diagrams and the identification of the possible macroscopic regimes emerging both in a single and in two identically coupled neural masses. In single populations SFA favors the emergence of population bursts in excitatory networks, while it hinders tonic population spiking for inhibitory ones. The symmetric coupling of two neural masses, in absence of adaptation, leads to the emergence of macroscopic solutions with broken symmetry, namely, chimera-like solutions in the inhibitory case and antiphase population spikes in the excitatory one. The addition of SFA leads to new collective dynamical regimes exhibiting cross-frequency coupling (CFC) among the fast synaptic timescale and the slow adaptation one, ranging from antiphase slow-fast nested oscillations to symmetric and asymmetric bursting phenomena. The analysis of these CFC rhythms in the θ-γ range has revealed that a reduction of SFA leads to an increase of the θ frequency joined to a decrease of the γ one. This is analogous to what has been reported experimentally for the hippocampus and the olfactory cortex of rodents under cholinergic modulation, which is known to reduce SFA.

Preauricular Incision Approach as a Management of Zygomaticomaxillary Complex Fracture Reduction: A Case Report

Introduction: A zygomatico maxillary complex fracture is a facial bone fracture that commonly occurs as a centrally and laterally protruding zygomatic area. The effective surgical approach and exact reduction of the displaced fracture is the most important task in the treatment of a zygomatic fracture, from the aesthetic point of view. Determination of surgical approach and the fixation point of zygomatic arch fracture is one of the most challenging procedure. The purpose of this case report is to find out that the preauricular incison approach is one of the effective methods for reduction of zygomaticomaxillary complex fracture. Case Report: A 53 years old male patient presented with right zygomatico maxillary complex fractures. Diagnosis of right side tetrapod zygomatico maxillary complex fracture deformity was done by clinical examination and confirmed by computed tomography which included 3-D reconstruction view. The authors performed 4-point fixation using the preauricular approach to counter the disadvantages of the coronal approach. The results and usefulness of preauricular approach with 4-point fixation are reported in this study. Conclusion: Preauricular incision is an effective surgical approach for the reduction of zygomatic arch fracture. 4-point fixation using the easier-to-manipulate preauricular approach would be more useful than the conventional method that uses the coronal approach. Satisfactory reduction that showed exact correction was observed. In an outpatient follow-up, no complication such as nonunion or malunion was found, and facial symmetry was also shown. In addition, the preauricular scar was hardly observed. Keywords: zygomaticomaxillary complex fracture, preauricular incision, reduction, fixation

On the Convergence of Orthogonal/Vector AMP: Long-Memory Message-Passing Strategy

Orthogonal/vector approximate message-passing (AMP) is a powerful message-passing (MP) algorithm for signal reconstruction in compressed sensing. This paper proves the convergence of Bayes-optimal orthogonal/vector AMP in the large system limit. The proof strategy is based on a novel long-memory (LM) MP approach: A first step is a construction of LM-MP that is guaranteed to converge systematically. A second step is a large-system analysis of LM-MP via an existing framework of state evolution. A third step is to prove the convergence of state evolution recursions for Bayes-optimal LM-MP via a new statistical interpretation of existing LM damping. The last is an exact reduction of the state evolution recursions for Bayes-optimal LM-MP to those for Bayes-optimal orthogonal/vector AMP. The convergence of the state evolution recursions for Bayes-optimal LM-MP implies that for Bayes-optimal orthogonal/vector AMP. Numerical simulations are presented to show the verification of state evolution results for damped orthogonal/vector AMP and a negative aspect of LM-MP in finite-sized systems.

Exact finite-dimensional reduction for a population of noisy oscillators and its link to Ott-Antonsen and Watanabe-Strogatz theories.

Populations of globally coupled phase oscillators are described in the thermodynamic limit by kinetic equations for the distribution densities or, equivalently, by infinite hierarchies of equations for the order parameters. Ott and Antonsen [Chaos 18, 037113 (2008)] have found an invariant finite-dimensional subspace on which the dynamics is described by one complex variable per population. For oscillators with Cauchy distributed frequencies or for those driven by Cauchy white noise, this subspace is weakly stable and, thus, describes the asymptotic dynamics. Here, we report on an exact finite-dimensional reduction of the dynamics outside of the Ott-Antonsen subspace. We show that the evolution from generic initial states can be reduced to that of three complex variables, plus a constant function. For identical noise-free oscillators, this reduction corresponds to the Watanabe-Strogatz system of equations [Watanabe and Strogatz, Phys. Rev. Lett. 70, 2391 (1993)]. We discuss how the reduced system can be used to explore the transient dynamics of perturbed ensembles.

An exact reduction technique for the k-Colour Shortest Path Problem

The k-Colour Shortest Path Problem is a variant of the classic Shortest Path Problem. This problem consists of finding a shortest path on a weighted edge-coloured graph, where the maximum number of different colours used in a feasible solution is fixed to be k. The k-CSPP has several real-world applications, particularly in network reliability. It addresses the problem of reducing the connection cost while improving the reliability of the network. In this work, we propose a heuristic approach, namely Colour-Constrained Dijkstra Algorithm (CCDA), which is able to produce effective solutions. We propose a graph reduction technique, namely the Graph Reduction Algorithm (GRA), which removes more than 90% of the nodes and edges from the input graph. Finally, using a Mixed-Integer Linear Programming (MILP) model, we present an exact approach, namely Reduced Integer Linear Programming Algorithm (RILP), that takes advantage of the heuristic CCDA and the GRA. Several tests were performed to verify the effectiveness of the proposed approaches. The computational results indicate that the produced approaches perform well, in terms of both the solution’s quality and computation times.

Physically Driven Exact Dimension Reduction of a Class of Nonlinear Multidimensional Systems Subjected to Additive White Noise

Physically Driven Exact Dimension Reduction of a Class of Nonlinear Multidimensional Systems Subjected to Additive White Noise