Regions Of Space Research Articles

OpenFold: retraining AlphaFold2 yields new insights into its learning mechanisms and capacity for generalization.

AlphaFold2 revolutionized structural biology with the ability to predict protein structures with exceptionally high accuracy. Its implementation, however, lacks the code and data required to train new models. These are necessary to (1) tackle new tasks, like protein-ligand complex structure prediction, (2) investigate the process by which the model learns and (3) assess the model's capacity to generalize to unseen regions of fold space. Here we report OpenFold, a fast, memory efficient and trainable implementation of AlphaFold2. We train OpenFold from scratch, matching the accuracy of AlphaFold2. Having established parity, we find that OpenFold is remarkably robust at generalizing even when the size and diversity of its training set is deliberately limited, including near-complete elisions of classes of secondary structure elements. By analyzing intermediate structures produced during training, we also gain insights into the hierarchical manner in which OpenFold learns to fold. In sum, our studies demonstrate the power and utility of OpenFold, which we believe will prove to be a crucial resource for the protein modeling community.

Imaging swiFTly: streaming widefield Fourier Transforms for large-scale interferometry

We describe a scalable distributed imaging algorithm framework for next-generation radio telescopes, managing the Fourier transform from apertures to sky (or vice versa) with a focus on minimising memory load, data transfers, and computation. Our algorithm uses smooth window functions to isolate the influence between specific regions of spatial-frequency and image space. This allows the distribution of image data between nodes and the construction of segments of frequency space exactly when and where needed. The developed prototype distributes terabytes of image data across many nodes, while generating visibilities at throughput and accuracy competitive with existing software. Scaling is demonstrated to be better than cubic in problem complexity (for baseline length and field of view), reducing the risk involved in growing radio astronomy processing to large telescopes like the Square Kilometre Array.

On the efficacy of surface-attached air bubbles as thermal insulators for pressure-driven internal flow

There exists much research examining the role of surface-attached air bubbles in drag reduction. Most of this literature considers isothermal flows and so ignores temperature differences, e.g. with the solid boundary. Here, we relax this assumption and ask whether surface-attached air bubbles may prove useful as thermal insulators, e.g. when the solid temperature differs from that of the cargo liquid (water). Theoretical and numerical solutions, e.g. for the variation of the Nusselt number with bubble thickness, are presented for cases characterized by a uniform surface heat flux (USF). We examine channel and pipe flow geometries, and consider instances where the net mass flow rate within the (continuous) air bubble is zero or non-zero. When the thermal boundary condition is changed to uniform surface temperature (UST), our analysis limits attention to numerical solutions. We identify and discuss a remarkable connection between the drag reduction problem and the USF thermal insulation problem: the proportional change of water temperature with bubble thickness is identical to the proportional change of drag. Also, and although our analysis is conducted in the ‘perfect plastron limit’, we can, e.g. by evaluating hydrodynamic and thermal slip lengths, contrast our work against related studies where heat transfer occurs through the ridges or pillars that affix the air layer in place. This comparison indicates that the oft-applied adiabatic interface assumption may prove restrictive in some regions of the parameter space. We conclude by examining the implications of our work in the context of UST micro-channels, which are relevant to various lab-on-a-chip technologies.

Some specific wormhole solutions in extended f(R,G,T) gravity

This research work provides an exhaustive investigation of the viability of different coupled wormhole (WH) geometries with the relativistic matter configurations in the [Formula: see text] extended gravity framework. We consider a specific model in the context of [Formula: see text]-gravity for this purpose. Also, we assume a static spherically symmetric spacetime geometry and a unique distribution of matter with a set of shape functions ([Formula: see text]) for analyzing different energy conditions. In addition to this, we examined WH-models in the equilibrium scenario by employing anisotropic fluid. The corresponding results are obtained using numerical methods and then presented using different plots. In this case, [Formula: see text] gravity generates additional curvature quantities, which can be thought of as gravitational objects that maintain irregular WH-situations. Based on our findings, we conclude that in the absence of exotic matter, WH can exist in some specific regions of the parametric space using modified gravity model as [Formula: see text].

Gravitational wave effects and phenomenology of a two-component dark matter model

We study an extension of the Standard Model (SM) which could have two candidates for dark matter (DM) including a Dirac fermion and a vector dark matter (VDM) under a new U(1) gauge group in the hidden sector. The model is classically scale-invariant and the electroweak symmetry breaks because of loop effects. We investigate the parameter space allowed by current experimental constraints and phenomenological bounds. We probe the parameter space of the model in the mass range 1<MV<5000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1< M_V<5000$$\\end{document} GeV and 1<Mψ<5000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<M_{\\psi }<5000$$\\end{document} GeV. It has been shown that there are many points in this mass range that are in agreement with all phenomenological constraints. The electroweak phase transition has been discussed and it has been shown that there is region in the parameter space of the model consistent with DM relic density and direct detection constraints that, at the same time, can lead to first-order electroweak phase transition. The gravitational waves produced during the phase transition could be probed by future space-based interferometers such as LISA and BBO.

Natural Concepts and the Economics of Cognition and Communication

AbstractThis article takes a cognitive approach to natural concepts. The aim is to introduce criteria that are evaluated with respect to how they support the cognitive economy of humans when using concepts in reasoning and communicating with them. I first present the theory of conceptual spaces as a tool for expressing the criteria. Then I introduce the central idea that natural concepts correspond to convex regions of a conceptual space. I argue that this criterion has far-reaching consequences as regards natural concepts. Partly following earlier work, I present some other criteria that further delimit the class of natural concepts. One of these is coherence, which does not seem to have been discussed previously. Finally, I show that convexity and other criteria make it possible to ensure that people mean the same thing when they communicate using concepts. Apart from its philosophical interest, the analysis presented in the article will be relevant for tasks of conceptual engineering in artificial systems that work with concepts.

Attractive (s)axions: cosmological trackers at the boundary of moduli space

We study the cosmological evolution of a FLRW universe dominated by the energy density of moduli close to asymptotic regions of moduli space. Due to the structure of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 1 SUGRA kinetic term, a saxion and an axion residing in the same chiral multiplet are (universally) coupled even if the latter is a flat direction of the potential, resulting in non-trivial dynamics. We generalise known results in the literature to the case of multiple moduli, showing the existence of various “tracker” attractor solutions where the relative energy densities of many components (axions included) stay in a fixed ratio throughout the evolution. We conclude with some phenomenological applications, relevant for both the early and late universe.

Synthesising Diverse and Discriminatory Sets of Instances using Novelty Search in Combinatorial Domains.

Gathering sufficient instance data to either train algorithm-selection models or understand algorithm footprints within an instance space can be challenging. We propose an approach to generating synthetic instances that are tailored to perform well with respect to a target algorithm belonging to a predefined portfolio but are also diverse with respect to their features. Our approach uses a novelty search algorithm with a linearly weighted fitness function that balances novelty and performance to generate a large set of diverse and discriminatory instances in a single run of the algorithm. We consider two definitions of novelty: (1) with respect to discriminatory performance within a portfolio of solvers; (2) with respect to the features of the evolved instances. We evaluate the proposed method with respect to its ability to generate diverse and discriminatory instances in two domains (knapsack and bin-packing), comparing to another well-known quality diversity method, Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) and an evolutionary algorithm that only evolves for discriminatory behaviour. The results demonstrate that the novelty search method outperforms its competitors in terms of coverage of the space and its ability to generate instances that are diverse regarding the relative size of the "performance gap" between the target solver and the remaining solvers in the portfolio. Moreover, for the Knapsack domain, we also show that we are able to generate novel instances in regions of an instance space not covered by existing benchmarks using a portfolio of state-of-the-art solvers. Finally, we demonstrate that the method is robust to different portfolios of solvers (stochastic approaches, deterministic heuristics and state-of-the-art methods), thereby providing further evidence of its generality.

Analysis of a detailed multi-stage model of stochastic gene expression using queueing theory and model reduction

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory.

Stability, Chemical Bonding, and Electron Lone Pair Localization in AsN at High Pressure by Density Functional Theory Calculations.

The covalent bonding framework of crystalline single-bonded cubic AsN, recently synthesized under high pressure and high temperature conditions in a laser-heated diamond anvil cell, is here studied by means of density functional theory calculations and compared to single crystal X-ray diffraction data. The precise localization of the nonbonding electron lone pairs and the determination of their distances and orientations are related to the presence of characteristic structural motifs and space regions of the unit cell dominated by repulsive electronic interactions, with the relative orientation of the electron lone pairs playing a key role in minimizing the energy of the structure. We find that the vibrational modes associated with the expression of the lone pairs are strongly localized, an observation that may have implications for the thermal conductivity of the compound. The results indicate the thermodynamic stability of the experimentally observed structure of AsN above ∼17 GPa, provide a detailed insight into the nature of the chemical bonding network underlying the formation of this compound, and open new perspectives to the design and high pressure synthesis of new pnictogen-based advanced materials for potential applications of energetic and technological relevance.

A novel metaheuristic based on object-oriented programming concepts for engineering optimization

This paper presents a novel, robust, efficient, and simple optimization algorithm called the Object-Oriented Programming Optimization Algorithm (OOPOA) for tackling constrained and unconstrained optimization problems. The algorithm is inspired by the inheritance concept of Object-Oriented programming languages, where the features of a class are classified into three types according to inheritance probability: public, private, and protected. The object-oriented programming inheritance concept is implemented in the algorithm to update the population for the next generations. The proposed algorithm ensures exploitation by selecting the solution with the highest fitness to be inherited in each iteration. It ensures exploration by applying a mutation process that helps explore wide regions in the search space. The performance of this technique is demonstrated by solving 34 different optimization tasks, including 20 standard benchmark problems, ten IEEE Congress of Evolutionary Computation benchmark test functions, and four constrained real-world engineering design problems.

MSE superiority of the unrestricted Stein-rule estimator in a regression model with a possible structural break

This paper investigates the estimation of a linear regression model with a possible structural break at a known point. We analytically derive the exact formulae of the MSE for the restricted SR and PSR estimators, which shrinks the OLS estimator toward the restriction of no structural break. We compare the MSE performance of restricted/unrestricted SR, PSR, and least squared estimators. We analytically show that the unrestricted SR estimator can have a smaller MSE than the restricted SR estimator even when the restriction is correct. Further, our numerical results show that the unrestricted PSR estimator has the best MSE performance over a wide region of parameter space. These results indicate that the use of the unrestricted PSR estimator is recommended even when a structural break may not exist, although the unrestricted PSR estimator does not take the possibility of no structural break into consideration.

Nonreciprocity and odd viscosity in chiral active fluids

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid [Formula: see text], quantum-Hall fluids, and recently in the context of chiral active matter. In most of these studies, odd terms in the viscosity obey Onsager reciprocal relations. Although this is expected in equilibrium systems, it is not obvious that Onsager relations hold in active materials. By directly coarse-graining the kinetic energy and independently using both the Poisson-bracket formalism and a kinetic theory derivation, we find that the appearance of a nonvanishing angular momentum density, which is a hallmark of chiral active materials, necessarily breaks Onsager reciprocal relations. This leads to a non-Hermitian dynamical matrix for the total hydrodynamic momentum and to the appearance of odd viscosity and other nondissipative contributions to the viscosity. Furthermore, by accounting for both the angular momentum density and interactions that lead to odd viscosity, we find regions in the parameter space in which 3D odd mechanical waves propagate and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting a possible nonreciprocal phase transition.

Laser induced spark ignition of a gaseous methane–oxygen model rocket combustor

The spatio-temporal evolution of laser induced spark ignition of non-premixed gaseous methane and oxygen is investigated. The reactants are injected into an optically accessible combustion chamber from an oxidizer centered shear-coaxial injector. High-speed schlieren imaging and measurements of laser energy deposited are used to characterize ignition behavior at various spark locations throughout the chamber. A spatial map of ignition probability is generated from tests at multiple axial and radial locations from the point of propellant injection. The rate of pressure rise from successful tests reveals two modes of ignition dependent on the location of the laser-induced breakdown, direct and indirect, based on laser-induced breakdown occurring within reactant jet or in the recirculation region, respectively. Physical processes occurring over multiple timescales throughout the direct ignition method are first discussed. Ignition outcomes associated with the indirect method are determined by the hydrodynamic ejection protruding from the laser spark, the behavior of which is explored in detail using flow statistics extracted from images taken at a single spark location. The spatial–temporal progression of this jet is found to be dependent on deposited laser energy, leading to a relationship between the amount of energy added to the flow and ignition outcome. General bounds for spark location, deposited laser energy, and ejection behavior are identified to predict ignition outcomes. Cases that are an exception from these bounds are investigated in detail to understand the cause of unique behavior. These cases lie within regions of the variable space that are susceptible to stochastic elements of the flow.Novelty and Significance Statement: This work investigates laser induced spark ignition of O2 and CH4 issuing from a shear-coaxial injector in a model rocket combustor. Probability of ignition as a function of deposited energy and spatial location is studied with high-speed schlieren imaging and pressure measurements. Two distinct ignition modes that have previously not been identified, direct and indirect, are dependent on the laser deposition location with respect to the reactant jet. For indirect cases, where laser deposition is at a distance from the reactants, the hydrodynamic jet ejection generated from the breakdown of the plasma plays a critical role on ignition probability. The behavior of the ejection jet is characterized to provide a phenomenological description of the ignition process. The results of this research show the important interaction between chemical, fluid dynamic, and thermodynamic processes and their impact on laser ignition.

EXPRESS: Admission Control in Multi-server Systems under Binary Reward Structure

We study a multi-server queueing system where a customer is satisfied (and generates a unit revenue) if their queueing time is at most a given constant. If the queueing time of the admitted customer exceeds this constant, the customer gets served, but is unsatisfied and generates no revenue. Such queueing systems arise in the context of modeling service systems where excessive delays are of concern. A key challenge is how to design an admission control policy to maximize the number of satisfied customers per unit time in the long run, assuming that we can observe the number of customers in the system at any time. We call this the binary reward structure system and show that a threshold-type admission policy is optimal. The optimal threshold policy has to be computed numerically. Hence we propose a square-root admission policy to approximate the optimal admission control policy, and compare the performance of these two policies. We derive an analytical upper bound on the performance of optimal admission control policy by deriving an optimal admission policy assuming we have full information over the queueing time of the admitted customers. This is equivalent to a queueing system where customers abandon the queue (i.e., leave without service) if their queueing time exceeds the given constant. We demonstrate that the optimal policy that includes customer abandonment, or alternatively, the optimal policy under full information, the optimal threshold policy, and the square-root admission policy, all exhibit identical performance in the asymptotic regions of the parameter space. Our numerical results indicate that the worst optimality gap of the square-root admission policy is within 3.9% of the optimal revenue, and implementing the square-root admission policy in the observable queueing system leads to a revenue loss that is at most 5.6% of the maximum possible revenue rate in the full information system. We also compare the binary reward structure with the more common linear reward structure where the system incurs holding cost per unit queueing time per customer. In addition, we also show that the analysis based on queueing time is applicable to the system time as well.

Earth’s Geomagnetic Environment—Progress and Gaps in Understanding, Prediction, and Impacts

Understanding of Earth’s geomagnetic environment is critical to mitigating the space weather impacts caused by disruptive geoelectric fields in power lines and other conductors on Earth’s surface. These impacts are the result of a chain of processes driven by the solar wind and linking Earth’s magnetosphere, ionosphere, thermosphere and Earth’s surface. Tremendous progress has been made over the last two decades in understanding the solar wind driving mechanisms, the coupling mechanisms connecting the magnetically controlled regions of near-Earth space, and the impacts of these collective processes on human technologies on Earth’s surface. Studies of solar wind drivers have been focused on understanding the responses of the geomagnetic environment to spatial and temporal variations in the solar wind associated with Coronal Mass Ejections, Corotating Interaction Regions, Interplanetary Shocks, High-Speed Streams, and other interplanetary magnetic field structures. Increasingly sophisticated numerical models are able to simulate the magnetospheric response to the solar wind forcing associated with these structures. Magnetosphere-ionosphere-thermosphere coupling remains a great challenge, although new observations and sophisticated models that can assimilate disparate data sets have improved the ability to specify the electrodynamic properties of the high latitude ionosphere. The temporal and spatial resolution needed to predict the electric fields, conductivities, and currents in the ionosphere is driving the need for further advances. These parameters are intricately tied to auroral phenomena—energy deposition due to Joule heating and precipitating particles, motions of the auroral boundary, and ion outflow. A new view of these auroral processes is emerging that focuses on small-scale structures in the magnetosphere and their ionospheric effects, which may include the rapid variations in current associated with geomagnetically induced currents and the resulting perturbations to geoelectric fields on Earth’s surface. Improvements in model development have paralleled the advancements in understanding, yielding coupled models that better replicate the spatial and temporal scales needed to simulate the interconnected domains. Many realizations of such multi-component systems are under development, each with its own limitations and advantages. Challenges remain in the ability of models to quantify uncertainties introduced by propagation of solar wind parameters, to account for numerical effects in model codes, and to handle the special conditions occurring during extreme events. The impacts to technical systems on the ground are highly sensitive to the local electric properties of Earth’s surface, as well as to the specific technology at risk. Current research is focused on understanding the characteristics of geomagnetic disturbances that are important for geomagnetically induced currents, the development of earth conductivity models, the calculation of geoelectric fields, and the modeling of induced currents in the different affected systems. Assessing and mitigating the risks to technical systems requires quantitative knowledge of the range of values to be expected under all possible geomagnetic and technical conditions. Considering the progress that has been made in studying the chain of events leading to hazardous geomagnetic disturbances, the path forward will require concerted efforts to reveal missing physics, improve modeling capabilities, and deploy new observational assets. New understanding should be targeted to accurately quantify solar wind driving, magnetosphere-ionosphere-thermosphere coupling, and the impacts on specific technologies. The research, modeling, and observations highlighted here provide a framework for constructing a plan by which the international science community can comprehensively address the growing threat to human technologies caused by geomagnetic disturbances.

An online transfer learning based multifactorial evolutionary algorithm for solving the clustered Steiner tree problem

The rapid increase in the number and computing power of devices interacting through the network over the past few years has led to a growing trend of decentralized clustering network architecture. The Clustered Steiner Tree Problem (CluSteiner) is a recently introduced NP-Hard problem and is assessed to be the core of efficient multicast routing in such networks. However, research on this problem in terms of theory and algorithmic design is still in its infancy as current solving approaches are limited in the literature. Lately, the Multifactorial Evolutionary Algorithm (MFEA) has been applied to solve several clustering-structure network design problems for the reason that these problems rarely exist independently and are often deployed concurrently in practice. To effectively transfer knowledge between problems while solving them simultaneously, this paper proposes an approach based on the novel data-driven MFEA-II to deal with the CluSteiner problem. In the proposal, an efficient encoding and a two-level decoding mechanism are introduced, combined with a module capable of online learning the amount of knowledge transferred between tasks that help the algorithm to explore potential regions of the search space. Experiments are undertaken on various test instances to evaluate the efficacy of the proposed algorithm. The empirical results indicate that our proposal can perform well on both metric and non-metric graphs with the statistical tests used to verify its efficiency over other baseline algorithms regarding the solution quality and convergence trend.

DyMMM-LEAPS: An ML-based framework for modulating evenness and stability in synthetic microbial communities

There have been a growing number of computational strategies to aid in the design of synthetic microbial consortia. A framework to identify regions in parametric space to maximize two essential properties, evenness and stability, is critical. In this study, we introduce DyMMM-LEAPS (Dynamic Multi-species Metabolic Modeling - Locating Evenness And stability in large Parametric Space), an extension of the DyMMM framework. Our method explores the large parametric space of genetic circuits in synthetic microbial communities to identify regions of evenness and stability. Due to the high computational costs of exhaustive sampling, we utilize adaptive sampling and surrogate modeling to reduce the number of simulations required to map the vast space. Our framework predicts engineering targets and computes their operating ranges to maximize the probability of the engineered community to have high evenness and stability. We demonstrate our approach by simulating five co-cultures and one three-strain culture with different social interactions (cooperation, competition, and predation) employing quorum-sensing based genetic circuits. In addition to guiding circuit tuning, our pipeline gives an opportunity for a detailed analysis of pockets of evenness and stability for the circuit under investigation, which can further help dissect the relationship between the two properties. DyMMM-LEAPS is easily customizable and can be expanded to a larger community with more complex interactions.

Artificial Broadcasts as Galactic Populations. II. Comparing Individualist and Collective Bounds on Broadcast Populations in Single Galaxies

The search for extraterrestrial intelligence includes efforts to constrain populations of artificial broadcasts in other galaxies. Previous efforts use individualist methods, searching for single broadcasts with high signal-to-noise ratio. These would be detected as observables with extreme values. This approach is limited to very bright broadcasts and also is subject to confusion, where a large number of broadcasts blend together to form a noise continuum. The mean value of the total emission provides an additional collective bound: the luminosity of the transmitters is no higher than the galaxy’s observed luminosity. Using the framework developed in Paper I, I evaluate how confusion affects individualist searches. I then compare individualist and collective approaches for radio broadcasts from the Milky Way, M31, and three Virgo Cluster elliptical galaxies. For current observations, confusion blurs narrowband radio broadcasts together in the Virgo ellipticals when there is one broadcast per gigahertz per 1000 stars. The collective bound implies fewer than ∼106(ℓ¯/1013W)−1 L-band broadcasts per star per gigahertz in the Milky Way wideband and is about 10 and 400 times stronger in M31 and M59, respectively. Applying the collective bound to the far-infrared–radio correlation yields constraints on radio broadcast populations in star-forming galaxies throughout the Universe. The collective bound allows us to rule out large regions of broadcast population parameter space even for distant galaxies. It also imposes constraints on gamma-ray, neutrino, and gravitational-wave broadcasts in the nearest galaxies.

Cluster-based regression using variational inference and applications in financial forecasting

This paper describes an approach to simultaneously identify clusters and estimate cluster-specific regression parameters from the given data. Such an approach can be useful in learning the relationship between input and output when the regression parameters for estimating output are different in different regions of the input space. Variational Inference (VI), a machine learning approach to obtain posterior probability densities using optimization techniques, is used to identify clusters of explanatory variables and regression parameters for each cluster. From these results, one can obtain both the expected value and the full distribution of predicted output. Other advantages of the proposed approach include the elegant theoretical solution and clear interpretability of results. The proposed approach is well-suited for financial forecasting where markets have different regimes (or clusters) with different patterns and correlations of market changes in each regime. In financial applications, knowledge about such clusters can provide useful insights about portfolio performance and identify the relative importance of variables in different market regimes. An illustrative example of predicting one-day S&P change is considered to illustrate the approach and compare the performance of the proposed approach with standard regression without clusters. Due to the broad applicability of the problem, its elegant theoretical solution, and the computational efficiency of the proposed algorithm, the approach may be useful in a number of areas extending beyond the financial domain.