Compact Constraints Research Articles

Dissipative dark cosmology: From early matter dominance to delayed compact objects

We demonstrate a novel mechanism for producing dark compact objects and black holes through a dark sector, where all the dark matter can be dissipative. Heavy dark sector particles with masses above 104 GeV can come to dominate the Universe and yield an early matter-dominated era before big bang nucleosynthesis (BBN). Density perturbations in this epoch can grow and collapse into tiny dark matter halos, which cool via self-interactions. The typical halo size is set by the Hubble length once perturbations begin growing, offering a straightforward prediction of the halo size and evolution depending on one’s choice of dark matter model. Once these primordial halos have formed, a thermal phase transition can then shift the Universe back into radiation domination and standard cosmology. These halos can continue to collapse after BBN, resulting in the late-time formation of fragmented dark compact objects and sub-solar-mass primordial black holes. We find that these compact objects can constitute a sizable fraction of all of dark matter. The resulting fragments can have masses between 1020 and 1032 g, with radii ranging from 10−2 to 105 m, while the black holes can have masses between 108 and 1034 g. Furthermore, a unique feature of this model is the late-time formation of black holes which can evaporate today. We compare where these objects lie with respect to current primordial black hole and massive (astrophysical) compact halo object constraints. Published by the American Physical Society 2024

Cryogenic systems of SuperKEKB final focusing superconducting magnets

SuperKEKB is an accelerator to collide electron and positron particles with a nano-beam collision scheme and equipped with two cryostats to accommodate 55 superconducting (SC) magnets for final focusing. Each cryostat is cooled by an independent cryogenic system employing a refrigerator of 250 W at 4.41 K and a subcooler to supply subcooled liquid helium (LHe), which absorbs heat leak by the relatively small sensible heat (∼2.4 J/g) with an acceptable temperature rise of 0.35 K from 4.41 K to 4.76 K (saturated temperature at 0.161 MPa). The associated limitation of the permissible heat leaks necessitated a careful cryostat design with comprehensive thermal considerations to reduce heat conduction and radiation and maintain stable cryogenic conditions of SC magnets. This paper presents the designs of the cryostats and cryogenic systems to address the technical challenges to cool SC magnets with the compact spatial constraints. Cryogenic systems were designed to supply a subcooled LHe flow of ∼20 g/s and to provide a mixed capacity of refrigeration and liquefaction loads. The liquefaction component amounts to 40 L/h (∼1.3 g/s), approximately half of the total refrigerator capacity to cool the vapor-cooled current leads of SC magnets, which is also found to significantly influence the total LHe flow (∼20 g/s) to cool the cryostats. Dedicated studies were performed to investigate the SC magnet temperature variations with the LHe flow, the system operation modes such as cooldown and quench of SC magnets, and to assess the heat leaks with local and global methods, which facilitate the practical operation of cryogenic systems for the SuperKEKB accelerator and are detailed in this paper.

Causal effective field theories

Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically symmetric scalar field background. We find that low energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from $2\ensuremath{\rightarrow}2$ scattering amplitude dispersion relations using full crossing symmetry.

Online-Updated High-Order Collaborative Networks for Single Image Deraining

Single image deraining is an important and challenging task for some downstream artificial intelligence applications such as video surveillance and self-driving systems. Most of the existing deep-learning-based methods constrain the network to generate derained images but few of them explore features from intermediate layers, different levels, and different modules which are beneficial for rain streaks removal. In this paper, we propose a high-order collaborative network with multi-scale compact constraints and a bidirectional scale-content similarity mining module to exploit features from deep networks externally and internally for rain streaks removal. Externally, we design a deraining framework with three sub-networks trained in a collaborative manner, where the bottom network transmits intermediate features to the middle network which also receives shallower rainy features from the top network and sends back features to the bottom network. Internally, we enforce multi-scale compact constraints on the intermediate layers of deep networks to learn useful features via a Laplacian pyramid. Further, we develop a bidirectional scale-content similarity mining module to explore features at different scales in a down-to-up and up-to-down manner. To improve the model performance on real-world images, we propose an online-update learning approach, which uses real-world rainy images to fine-tune the network and update the deraining results in a self-supervised manner. Extensive experiments demonstrate that our proposed method performs favorably against eleven state-of-the-art methods on five public synthetic datasets and one real-world dataset.

Dark photon bursts from compact binary systems and constraints

In this work, we consider the burst signal of the dark photon, the hypothetical vector boson of the $U(1)_B$ or $U(1)_{B-L}$ gauge group, generated by a compact binary star system. The absence of the signal in the laser interferometer puts bounds on the coupling constant $\epsilon$ to the ordinary matter. It turns out that if the dark photon is massless, $\epsilon^2$ is on the order of $10^{-37}-10^{-33}$ at most; in the massive case, the upper bound of $\epsilon^2$ is about $10^{-38}-10^{-31}$ in the mass range from $10^{-19}$ eV to $10^{-11}$ eV. These are the first bounds derived from the interferometer observations independent of the assumption of dark photons being dark matter.

How does dark matter affect compact star properties and high density constraints of strongly interacting matter

We study the impact of asymmetric bosonic dark matter on neutron star properties, including possible changes of tidal deformability, maximum mass, radius, and matter distribution inside the star. The conditions at which dark matter particles tend to condensate in the star’s core or create an extended halo are presented. We show that dark matter condensed in a core leads to a decrease of the total gravitational mass and tidal deformability compared to a pure baryonic star, which we will perceive as an effective softening of the equation of state. On the other hand, the presence of a dark matter halo increases those observable quantities. Thus, observational data on compact stars could be affected by accumulated dark matter and, consequently, constraints we put on strongly interacting matter at high densities. To confirm the presence of dark matter in the compact star’s interior, and to break the degeneracy between the effect of accumulated dark matter and strongly interacting matter properties at high densities, several astrophysical and GW tests are proposed.

Numerical Identification of Nonlocal Potentials in Aggregation

Aggregation equations are broadly used to model population dynamics with nonlocal interactions, characterized by a potential in the equation. This paper considers the inverse problem of identifying the potential from a single noisy spatial-temporal process. The identification is challenging in the presence of noise due to the instability of numerical differentiation. We propose a robust model-based technique to identify the potential by minimizing a regularized data fidelity term, and regularization is taken as the total variation and the squared Laplacian. A split Bregman method is used to solve the regularized optimization problem. Our method is robust to noise by utilizing a Successively Denoised Differentiation technique. We consider additional constraints such as compact support and symmetry constraints to enhance the performance further. We also apply this method to identify time-varying potentials and identify the interaction kernel in an agent-based system. Various numerical examples in one and two dimensions are included to verify the effectiveness and robustness of the proposed method.

Optimal Power Allocation for Cooperative Pattern Division Multiple Access Systems

This study focuses on the power allocation (PA) problem in code division multiple access (PDMA) networks with amplify-and-forward (AF) relays. We provide two wireless communication technical performance indexes, which are system throughput and outage probability. A multiobjective version of particle swarm optimization is proposed to solve Pareto-optimal solutions for optimal PA problems. A novel programming model is built based on improvement of constraint functions, and the accuracy and efficiency of solution can be improved via compact constraints. The technique for order preference by similarity to an ideal solution is proposed to balance the performance indicators, which include outage probability and system throughput. It has been calculated that the proposed approach for optimal PA is verified and performs better than a genetic algorithm approach.

A class of smooth exact penalty function methods for optimization problems with orthogonality constraints

ABSTRACT Updating the augmented Lagrangian multiplier by closed-form expression yields efficient first-order infeasible approach for optimization problems with orthogonality constraints. Hence, parallelization becomes tractable in solving this type of problems. Inspired by this closed-form updating scheme, we propose a novel penalty function with compact convex constraints (PenC). We show that PenC can act as an exact penalty model which shares the same global minimizers as the original problem with orthogonality constraints. Based on PenC, we first propose a first-order algorithm called PenCF and establish its global convergence and local linear convergence rate under some mild assumptions. For the case that the computation and storage of Hessian is achievable, and we pursue high precision solution and fast local convergence rate, a second-order approach called PenCS is proposed for solving PenC. To avoid expensive calculation or solving a hard subproblem in computing the Newton step, we propose a new strategy to do it approximately which still leads to quadratic convergence locally. Moreover, the main iterations of both PenCF and PenCS are orthonormalization-free and hence parallelizable. Numerical experiments illustrate that PenCF is comparable with the existing first-order methods. Furthermore, PenCS shows its stability and high efficiency in obtaining high precision solution comparing with the existing second-order methods.

Thermohydraulic and entropy characteristics of Al2O3‐water nanofluid in a ribbed interrupted microchannel heat exchanger

AbstractIn this study, an interrupted microchannel heat sink with rib turbulators was studied for its thermohydraulic effectiveness and entropy generation in a compact space. The rib edges are modified to enhance the overall functioning of the system by reducing the pressure drop. The working fluid used was Al2O3‐water nanofluid, and increasing the Reynolds number and nanoparticle concentration triggered a reduction in the heat sink's maximum temperature. These also offer a decrease in resistance to heat transfer, and there is an improvement in the evenness of the temperature of the interrupted microchannel heat sink, as regions with the likelihood of hot spot reduced drastically. At Re = 100, increasing the nanoparticle concentration from 0% to 4% enhanced the heat transfer coefficient by 38.41% for the interrupted microchannel heat sink‐base (IMCH‐B) configuration. Under similar conditions, the convective heat transfer coefficient for the interrupted microchannel heat sink‐fillet (IMCH‐F) increased by 43.69%. Furthermore, at 0.5% concentration, changing the Reynolds number from 100 to 700 augmented the heat transfer coefficient by 70.65%. Thus, the maximum temperature of the substrate's bottom surface was reduced by 53.83°C when the system was operated at Re = 700 and nanoparticle concentration of 4%. The IMCH‐C also showed relatively close results at all observed volume fractions. For the IMCH‐C, the maximum temperature of the bottom surface was reduced by 41.98°C at Re = 700 when compared with Re = 100% and 4% concentration. Although at high Reynolds numbers and concentrations, the pressure drops are higher, the performance enhancement criteria prove that the nanofluid is superior to water and the edge modifications show significant performance improvement. More importantly, the IMCH‐F heat sink showed the optimum performance based on the performance evaluation criteria at Re = 300 and (ie, at this point, the heat transfer coefficient is maximum and the pressure drop is minimum). On the other hand, the optimal thermodynamic performance was observed at Re = 700 and . The numerical results demonstrated a potential way to exploit nano‐suspensions for thermal applications, especially for high‐energy flux systems with compact space constraints.

Generation of Scale-Invariant Sequential Activity in Linear Recurrent Networks.

Sequential neural activity has been observed in many parts of the brain and has been proposed as a neural mechanism for memory. The natural world expresses temporal relationships at a wide range of scales. Because we cannot know the relevant scales a priori, it is desirable that memory, and thus the generated sequences, is scale invariant. Although recurrent neural network models have been proposed as a mechanism for generating sequences, the requirements for scale-invariant sequences are not known. This letter reports the constraints that enable a linear recurrent neural network model to generate scale-invariant sequential activity. A straightforward eigendecomposition analysis results in two independent conditions that are required for scale invariance for connectivity matrices with real, distinct eigenvalues. First, the eigenvalues of the network must be geometrically spaced. Second, the eigenvectors must be related to one another via translation. These constraints are easily generalizable for matrices that have complex and distinct eigenvalues. Analogous albeit less compact constraints hold for matrices with degenerate eigenvalues. These constraints, along with considerations on initial conditions, provide a general recipe to build linear recurrent neural networks that support scale-invariant sequential activity.

SVLA: A compact supervoxel segmentation method based on local allocation

With the development of three-dimensional (3D) point cloud acquisition technologies, supervoxels have become increasingly important, as they provide compact and uniform representations. In this study, a novel supervoxel segmentation method, supervoxels based on local allocation (SVLA), is proposed. SVLA is composed of three steps, namely extreme point determination, local allocation (LA), and connectivity insurance. LA defines a novel cost function for preserving instance boundaries and enforces local minimization. To test the performance of SVLA, the non-compactness error (NCE) is newly defined to evaluate the compactness, and three commonly used evaluation metrics are employed. Both indoor and outdoor datasets are utilized to perform the experiments. Based on the visual and quantitative analysis of the segmentation results, SVLA demonstrates fulfillment of boundary adherence, compact constraints, and low computational complexity. Compared to state-of-the-art algorithms, SVLA yields superior results, especially with regard to indoor point clouds.

Effect of stirrup iron style on normal forces and rider position during the posting trot

We consider the controllability problem for finite-dimensional linear autonomous control systems, under state constraints but without imposing any control constraint. It is well known that, under the classical Kalman condition, in the absence of constraints on the state and the control, one can drive the system from any initial state to any final one in an arbitrarily small time. Furthermore, it is also well known that there is a positive minimal time in the presence of compact control constraints. We prove that, surprisingly, a positive minimal time may be required as well under state constraints, even if one does not impose any restriction on the control. This may even occur when the state constraints are unilateral, like the nonnegativity of some components of the state, for instance. Using the Brunovsky normal forms of controllable systems, we analyze this phenomenon in detail, that we illustrate by several examples. We discuss some extensions to nonlinear control systems and formulate some challenging open problems.

Minimal controllability time for finite-dimensional control systems under state constraints

We consider the controllability problem for finite-dimensional linear autonomous control systems, under state constraints but without imposing any control constraint. It is well known that, under the classical Kalman condition, in the absence of constraints on the state and the control, one can drive the system from any initial state to any final one in an arbitrarily small time. Furthermore, it is also well known that there is a positive minimal time in the presence of compact control constraints. We prove that, surprisingly, a positive minimal time may be required as well under state constraints, even if one does not impose any restriction on the control. This may even occur when the state constraints are unilateral, like the nonnegativity of some components of the state, for instance. Using the Brunovsky normal forms of controllable systems, we analyze this phenomenon in detail, that we illustrate by several examples. We discuss some extensions to nonlinear control systems and formulate some challenging open problems.

Global Convergence of ADMM in Nonconvex Nonsmooth Optimization

In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, $\phi(x_0,\ldots,x_p,y)$, subject to coupled linear equality constraints. Our ADMM updates each of the primal variables $x_0,\ldots,x_p,y$, followed by updating the dual variable. We separate the variable $y$ from $x_i$'s as it has a special role in our analysis. The developed convergence guarantee covers a variety of nonconvex functions such as piecewise linear functions, $\ell_q$ quasi-norm, Schatten-$q$ quasi-norm ($0<q<1$), minimax concave penalty (MCP), and smoothly clipped absolute deviation (SCAD) penalty. It also allows nonconvex constraints such as compact manifolds (e.g., spherical, Stiefel, and Grassman manifolds) and linear complementarity constraints. Also, the $x_0$-block can be almost any lower semi-continuous function. By applying our analysis, we show, for the first time, that several ADMM algorithms applied to solve nonconvex models in statistical learning, optimization on manifold, and matrix decomposition are guaranteed to converge. Our results provide sufficient conditions for ADMM to converge on (convex or nonconvex) monotropic programs with three or more blocks, as they are special cases of our model. ADMM has been regarded as a variant to the augmented Lagrangian method (ALM). We present a simple example to illustrate how ADMM converges but ALM diverges with bounded penalty parameter $\beta$. Indicated by this example and other analysis in this paper, ADMM might be a better choice than ALM for some nonconvex \emph{nonsmooth} problems, because ADMM is not only easier to implement, it is also more likely to converge for the concerned scenarios.

Methods based on 1D homography for camera calibration with 1D objects.

This paper focuses on camera calibration with one-dimensional (1D) objects, and novel methods are proposed in this paper. Different from the known 1D object-based camera calibration algorithms, which define the camera coordinate system as the world coordinate system, we assume that the 1D calibration object is located along the X axis of the world coordinate system. Based on this new model, a 3×2 1D homography is defined to relate the points in the 1D objects to the perspective image points thereof. Then, the basic constraint for camera calibration using 1D objects from a single image is derived. Subsequently, two existing motions, namely, rotating around a fixed point and moving on a plane, are discussed, and new algorithms are proposed. In our methods, if the number of points in the 1D objects is more than three, more compact constraints can be obtained when the 1D objects rotate around a fixed point. In the case of planar motion, the estimation of vanishing points is not needed, and the calibration accuracy is significantly improved. Finally, both computer simulations and experiments are performed to validate the effectiveness and robustness of our algorithms.

Control with a Guide in the Guarantee Optimization Problem under Functional Constraints on the Disturbance

A motion control problem for a dynamic system under disturbances is considered on a finite time interval. There are compact geometric constraints on the values of the control and disturbance. The equilibrium condition in the small game is not assumed. The aim of the control is to minimize a given terminal performance index. The guaranteed result optimization problem is posed in the context of the game-theoretical approach. In the case when realizations of the disturbance belong to some a priori unknown compact subset of L1 (the space of functions that are Lebesgue summable with the norm), we propose a new discrete-time control procedure with a guide. The proximity between the motions of the system and the guide is provided by the dynamic reconstruction of the disturbance. The quality of the control process is achieved by using an optimal counter-strategy in the guide. Conditions on the equations of motion under which this procedure ensures an optimal guaranteed result in the class of quasi-strategies are given. The scheme of the proof makes it possible to estimate the deviation of the realized value of the performance index from the value of the optimal result depending on the discretization parameter. Illustrative examples are given.

Toward a Galactic Distribution of Planets. I. Methodology and Planet Sensitivities of the 2015 High-cadence Spitzer Microlens Sample

Abstract We analyze an ensemble of microlensing events from the 2015 Spitzer microlensing campaign, all of which were densely monitored by ground-based high-cadence survey teams. The simultaneous observations from Spitzer and the ground yield measurements of the microlensing parallax vector , from which compact constraints on the microlens properties are derived, including ≲25% uncertainties on the lens mass and distance. With the current sample, we demonstrate that the majority of microlenses are indeed in the mass range of M dwarfs. The planet sensitivities of all 41 events in the sample are calculated, from which we provide constraints on the planet distribution function. In particular, assuming a planet distribution function that is uniform in , where q is the planet-to-star mass ratio, we find a 95% upper limit on the fraction of stars that host typical microlensing planets of 49%, which is consistent with previous studies. Based on this planet-free sample, we develop the methodology to statistically study the Galactic distribution of planets using microlensing parallax measurements. Under the assumption that the planet distributions are the same in the bulge as in the disk, we predict that ∼1/3 of all planet detections from the microlensing campaigns with Spitzer should be in the bulge. This prediction will be tested with a much larger sample, and deviations from it can be used to constrain the abundance of planets in the bulge relative to the disk.

Quark-nuclear hybrid star equation of state with excluded volume effects

A two-phase description of the quark-nuclear matter hybrid equation of state that takes into account the effect of excluded volume in both the hadronic and the quark matter phases is introduced. The nuclear phase manifests a reduction of the available volume as density increases, leading to a stiffening of the matter. The quark matter phase displays a reduction of the effective string tension in the confining density functional from available volume contributions. The nuclear equation of state is based upon the relativistic density functional model DD2 with excluded volume. The quark matter is based upon a mean-field modification to the free fermi gas and will be discussed in greater detail. The interactions are decomposed into mean scalar and vector components. The scalar interaction is motivated by a string potential between quarks, whereas the vector interaction potential is motivated by higher order interactions of quarks leading to an increased stiffening at high densities. As an application, we consider matter under compact star constraints of electric neutrality and $\beta$-equilibrium. We obtain mass-radius relations for hybrid stars that form a third family, disconnected from the purely hadronic star branch, and fulfill the $2M_\odot$ constraint.

A Probabilistic Analysis of Positional Errors on Satellite Remote Sensing Data Using Scattered Interpolation

With the recent development of CubeSats, several ultracompact, low cost, and rapidly deployable satellites have been developed for earth observation missions. Because of the geometry of the acquisition process, measurements are irregularly sampled, whereas in meteorological applications, data are preferred on a regular grid. This problem is further complicated by the fact that, due to CubeSats’ compact sizes and constraints, such as limited power, errors occur in geolocation calibration, resulting in positional errors. In this letter, we analyze how the commonly used triangulation-based linear data interpolation scheme behaves under probabilistic models for the positional errors. The derived distribution of interpolation error caused by positional error is intractable even under a Gaussian distribution for positional errors. To address this problem, we developed an analytical closed-form solution to the first two moments of the interpolation error. Using models for positional errors motivated by our prior work, experimental results show that, compared with the first-order linear model, the second-order one provides a better approximation in terms of the mean and variance, which is very close to that is obtained using more computationally intensive Monte Carlo simulations. This model also allows for the closed-form calculation of mean squared interpolation error, which can be of use in the context of system design where the impact of positional errors on remote sensing products must be considered.