Extra Constraints Research Articles

Inverting Cryptographic Hash Functions via Cube-and-Conquer

MD4 and MD5 are fundamental cryptographic hash functions proposed in the early 1990s. MD4 consists of 48 steps and produces a 128-bit hash given a message of arbitrary finite size. MD5 is a more secure 64-step extension of MD4. Both MD4 and MD5 are vulnerable to practical collision attacks, yet it is still not realistic to invert them, i.e., to find a message given a hash. In 2007, the 39-step version of MD4 was inverted by reducing to SAT and applying a CDCL solver along with the so-called Dobbertin’s constraints. As for MD5, in 2012 its 28-step version was inverted via a CDCL solver for one specified hash without adding any extra constraints. In this study, Cube-and-Conquer (a combination of CDCL and lookahead) is applied to invert step-reduced versions of MD4 and MD5. For this purpose, two algorithms are proposed. The first one generates inverse problems for MD4 by gradually modifying the Dobbertin’s constraints. The second algorithm tries the cubing phase of Cube-and-Conquer with different cutoff thresholds to find the one with the minimum runtime estimate of the conquer phase. This algorithm operates in two modes: (i) estimating the hardness of a given propositional Boolean formula; (ii) incomplete SAT solving of a given satisfiable propositional Boolean formula. While the first algorithm is focused on inverting step-reduced MD4, the second one is not area-specific and is therefore applicable to a variety of classes of hard SAT instances. In this study, 40-, 41-, 42-, and 43-step MD4 are inverted for the first time via the first algorithm and the estimating mode of the second algorithm. Also, 28-step MD5 is inverted for four hashes via the incomplete SAT solving mode of the second algorithm. For three hashes out of them, it is done for the first time.

UAV p­­­arcel Delivery System with Deep Reinforcement Learning Based Collision Avoidance and Route Optimization

Unmanned Aerial Vehicles (UAVs), or drones, have recently become a favorable solution for fast parcel delivery due to their maneuverability and advances in navigation technologies. With the limitation of battery capacity and payload of drones, it is crucial to consider both efficiency and cost while conducting the tasks. Meanwhile, UAVs should not collide with each other while traveling to customers. In this article, we propose a UAV parcel delivery system involving deep reinforcement learning (DRL) approach for collision avoidance and a genetic algorithm for route optimization. Specifically, a delivery center generates near-optimal routes, loading UAV with parcels according to demands. Each UAV takes charge of delivering packages in compliance with the assigned route while avoiding collision with each other. We utilize DRL to achieve collision avoidance without having prior knowledge about the trajectories of other UAVs. Additionally, we adopt a genetic algorithm to obtain the lowest energy cost path for each UAV. To find such an optimized path, we solve a capacitated vehicle routing problem (CVRP) with a modified cost function and extra constraints. Realistic simulations using a physics engine and software-in-the-loop (SITL) are conducted to evaluate the feasibility of the proposed methods.

The stringy S-matrix bootstrap: maximal spin and superpolynomial softness

We explore the space of meromorphic amplitudes with extra constraints coming from the shape of the leading Regge trajectory. This information comes in two guises: it bounds the maximal spin of exchanged particles of a given mass; it leads to sum rules obeyed by the discontinuity of the amplitude, which express the softness of scattering at high energies. We assume that the leading Regge trajectory is linear, and we derive bounds on the low-energy Wilson coefficients using the dual and primal approaches. For the graviton-graviton scattering in four dimensions, the maximal spin constraint leads to slightly more stringent bounds than those that follow from general constraints of analyticity, crossing, and unitarity. The exponential softness at high energies is manifest in our primal approach and is not used in our implementation of the dual approach. Nevertheless, we observe the agreement between the bounds obtained from both. We conclude that high-energy superpolynomial softness does not leave an obvious imprint on the low-energy observables. We exhibit a unitary three-parameter deformation of the Veneziano amplitude for the open string case. It has a novel, exponentially soft behavior at high energies and fixed angles. We generalize the previous analysis of this regime and present a stringy version of the lower bound on high-energy, fixed-angle scattering by Cerulus and Martin.

Marcus Stochastic Differential Equations: Representation of Probability Density

Marcus stochastic delay differential equations are often used to model stochastic dynamical systems with memory in science and engineering. It is challenging to study the existence, uniqueness, and probability density of Marcus stochastic delay differential equations, due to the fact that the delays cause very complicated correction terms. In this paper, we identify Marcus stochastic delay differential equations with some Marcus stochastic differential equations without delays but subject to extra constraints. This helps us to obtain the following two main results: (i) we establish a sufficient condition for the existence and uniqueness of the solution to the Marcus delay differential equations; and (ii) we establish a representation formula for the probability density of the Marcus stochastic delay differential equations. In the representation formula, the probability density for Marcus stochastic differential equations with memory is analytically expressed in terms of probability density for the corresponding Marcus stochastic differential equations without memory.

Symmetries of modified Dirac operators in supergravity flux backgrounds

Modifications of Dirac operators in supergravity flux backgrounds are considered. Modified spin curvature operators and squares of modified Dirac operators corresponding to Schrödinger-Lichnerowicz-like formulas are obtained for different types of flux modifications. Symmetry operators of modified massless and massive Dirac equations are found in terms of modified Killing-Yano and modified conformal Killing-Yano forms. Extra constraints for symmetry operators in terms of different types of fluxes and modified Killing-Yano forms are determined.

The Euler non-mixing made easy

The non-transitivity without extra constraints in the Euler equation in any dimension is almost evident and can be derived, e.g. from Morse theory.

Resilient inverse optimal control for tracking: Overcoming process noise challenges

This paper studies the Inverse Optimal Control (IOC), aiming to identify the underlying cost functions using observed optimal control paths. An innovative IOC algorithm is developed in this paper by leveraging the closed-loop control law of optimal tracking control, without needing to consider any prior knowledge of the process noise. More explicitly, a convex optimization problem is formulated for the IOC problem by encompassing various linear constraints. The contributions of our work include: (i) Robustly handling process noise, ensuring accuracy without excessive data. (ii) Deriving linear conditions for optimal tracking control law, leading to a closed-form IOC solution that can yield the global optimal solution under sufficient conditions. (iii) No extra LMI constraints are needed when dealing with diverse reference signals. The paper concludes by demonstrating our approach’s effectiveness through simulations and comparisons with baseline methods.

Self-consistent field theory for loop-containing polymers: A general algorithm for path-determination

An algorithm was developed for self-consistent field theory (SCFT) simulations of loop-containing polymers (LCPs), where the total number of independent loops (fundamental cycles in the polymer structure) is characterized by the “cycle rank.” Although various multi-ring and cage-like polymers have been reported, there is no explicit SCFT scheme for LCPs with multiple loops. An LCP was cut to open its fundamental cycles to form a pseudo-tree-like polymer. Conventional SCFT calculations for pseudo-tree-like polymers require extra spatial constraints on the pseudo-free endpoints generated by opening the fundamental cycle, which increases the computational cost. A reduction in the computational cost was observed, and the algorithm was applied to microphase-separated structures of small LCPs.

Learning Oriented Object Detection via Naive Geometric Computing.

Detecting oriented objects along with estimating their rotation information is one crucial step for image analysis, especially for remote sensing images. Despite that many methods proposed recently have achieved remarkable performance, most of them directly learn to predict object directions under the supervision of only one (e.g., the rotation angle) or a few (e.g., several coordinates) groundtruth (GT) values individually. Oriented object detection would be more accurate and robust if extra constraints, with respect to proposal and rotation information regression, are adopted for joint supervision during training. To this end, we propose a mechanism that simultaneously learns the regression of horizontal proposals, oriented proposals, and rotation angles of objects in a consistent manner, via naive geometric computing, as one additional steady constraint. An oriented center prior guided label assignment strategy is proposed for further enhancing the quality of proposals, yielding better performance. Extensive experiments on six datasets demonstrate the model equipped with our idea significantly outperforms the baseline by a large margin and several new state-of-the-art results are achieved without any extra computational burden during inference. Our proposed idea is simple and intuitive that can be readily implemented. Source codes are publicly available at: https://github.com/wangWilson/CGCDet.git.

Distributed Transactions in Microservice Architecture: Informed Decision-making Strategies

The emergence of microservice architecture has revolutionized software development practices by decentralizing components, facilitating scalability, and enabling agility in system design and deployment. There are some benefits of incorporating microservices instead of a single server, however, distributed components introduce extra constraints and complexities in maintaining data consistency as well. As microservices interact independently, coordinating data updates across multiple services becomes challenging, particularly in scenarios where transactional integrity is required. Distributed transactions are one of the solutions for ensuring data consistency across services. Regardless of effectiveness distributed transactions entail different trade-offs and performance implications. Those trade-offs are not always justified. This study highlights the need for a nuanced understanding of distributed transactions in microservices by revisiting challenges in managing distributed transactions within data storage systems. It also represents existing solutions to the different distributed transaction methods. In this paper, through experiments comparing microservices and monolithic systems, the impact of distributed transactions on system performance is evaluated, giving intuition about consequences when a single data source transaction is migrated to the distributed environment. This research also contributes to enhancing understanding and decision-making regarding the utilization of distributed transactions in a microservices architecture. Ultimately, this paper presents an optimized decision-framework for the application of distributed transactions in microservices architecture, aiming to simplify and expedite processes of software architecture for software engineers, solution architects, and developers.

Structural iterative rounding for generalized k-median problems

AbstractThis paper considers approximation algorithms for generalized k-median problems. These problems can be informally described as k-median with a constant number of extra constraints, and includes k-median with outliers, and knapsack median. Our first contribution is a pseudo-approximation algorithm for generalized k-median that outputs a 6.387-approximate solution, with a constant number of fractional variables. The algorithm builds on the iterative rounding framework introduced by Krishnaswamy, Li, and Sandeep for k-median with outliers as reported (Krishnaswamy et al. in: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018). The main technical innovation is allowing richer constraint sets in the iterative rounding and using the structure of the resulting extreme points. Using our pseudo-approximation algorithm, we give improved approximation algorithms for k-median with outliers and knapsack median. This involves combining our pseudo-approximation with pre- and post-processing steps to round a constant number of fractional variables at a small increase in cost. Our algorithms achieve approximation ratios $$6.994 + \epsilon $$ 6.994 + ϵ and $$6.387 + \epsilon $$ 6.387 + ϵ for k-median with outliers and knapsack median, respectively. These improve on the best-known approximation ratio $$7.081 + \epsilon $$ 7.081 + ϵ for both problems as reported (Krishnaswamy et al. in: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018).

Universal deformations and inhomogeneities in isotropic Cauchy elasticity

For a given class of materials, universal deformations are those deformations that can be maintained in the absence of body forces and by applying solely boundary tractions. For inhomogeneous bodies, in addition to the universality constraints that determine the universal deformations, there are extra constraints on the form of the material inhomogeneities—universal inhomogeneity constraints. Those inhomogeneities compatible with the universal inhomogeneity constraints are called universal inhomogeneities. In a Cauchy elastic solid, stress at a given point and at an instance of time is a function of strain at that point and that exact moment in time, without any dependence on prior history. A Cauchy elastic solid does not necessarily have an energy function, i.e. Cauchy elastic solids are, in general, non-hyperelastic (or non-Green elastic). In this paper, we characterize universal deformations in both compressible and incompressible inhomogeneous isotropic Cauchy elasticity. As Cauchy elasticity includes hyperelasticity, one expects the universal deformations of Cauchy elasticity to be a subset of those of hyperelasticity both in compressible and incompressible cases. It is also expected that the universal inhomogeneity constraints to be more stringent than those of hyperelasticity, and hence, the set of universal inhomogeneities to be smaller than that of hyperelasticity. We prove the somewhat unexpected result that the sets of universal deformations of isotropic Cauchy elasticity and isotropic hyperelasticity are identical, in both the compressible and incompressible cases. We also prove that their corresponding universal inhomogeneities are identical as well.

Interleaved ZVS DC‐DC converter with ultrahigh step‐down and flexible gain

AbstractThis paper proposes a novel non‐isolated ultrahigh step‐down interleaved DC‐DC converter with an extremely extended duty cycle based on the series capacitor and coupled‐inductor techniques. The proposed converter utilizes a three‐winding coupled inductor (TWCI) to enhance the step‐down conversion ratio. In contrast to conventional coupled inductor‐based step‐down converters, its voltage gain improves as the turn ratio approaches unity. Consequently, coupled inductors have significantly lower winding losses. Furthermore, there is no extra constraint on the turn ratio of the TWCI. It results in a highly flexible voltage gain and more design freedom. Other advantages of the employed series capacitor and coupled inductor techniques can be listed as, zero voltage switching (ZVS) condition for all switches, significant reduction of the total switching device power (SDP) and recovery of the energy of leakage inductors. They all reduce power losses and costs. Steady‐state analysis, derivation of voltage gain and design considerations are discussed in detail. Finally, a 200 W, 400‐to‐12 V experimental prototype is implemented to verify the effectiveness and feasibility of the proposed converter.

Linear and Nonlinear Formulation of Phase Field Model with Generalized Polynomial Degradation Functions for Brittle Fractures

The classical phase field model has wide applications for brittle materials, but nonlinearity and inelasticity are found in its stress–strain curve. The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive, but stiffness reduction happens even at low strain. In this paper, generalized polynomial degradation functions are investigated to solve this problem. The first derivative of degradation function at zero phase is added as an extra constraint, which renders higher-order polynomial degradation function and nonlinear formulation of phase field. Compared with other degradation functions (like algebraic fraction function, exponential function, and trigonometric function), this polynomial degradation function enables phase in [0, 1] (should still avoid the first derivative of degradation function at zero phase to be 0), so there is no Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document} convergence problem. The good and meaningful finding is that, under the same fracture strength, the proposed phase field model has a larger length scale, which means larger element size and better computational efficiency. This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton–Raphson method. A tensile test shows that the first derivative of degradation function at zero phase does impact stress–strain curve. Mode I, mode II, and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.

Trinity IV: predictions for supermassive black holes at z ≳ 6

ABSTRACT We present predictions for the high-redshift halo–galaxy–supermassive black hole (SMBH) connection from the Trinity model. Matching a comprehensive compilation of galaxy (0 ≤ z ≤ 13) and SMBH data sets (0 ≤ z ≤ 6.5), Trinity finds: (1) The number of SMBHs with M• > 109 M⊙ in the observable Universe increases by five orders of magnitude from z ∼ 10 to z ∼ 2, and by another factor of ∼3 from z ∼ 2 to z = 0; (2) The M• > 109 and 1010 M⊙ SMBHs at z ∼ 6 live in haloes with ∼(2 − 3) and (3 − 5) × 1012 M⊙; (3) the newly discovered JWST AGN candidates at 7 ≲ z ≲ 11 are overmassive compared to the intrinsic SMBH mass–galaxy mass relation from Trinity, but they are still broadly consistent with Trinity predictions for flux limited AGN samples with Lauer bias. This bias favours the detection for overmassive SMBHs due to higher luminosities at a fixed Eddington ratio. However UHZ1’s M•/M* ratio is still some 1 dex higher than Trinity AGNs, indicating a discrepancy; (4) Trinity underpredicts the number densities of GN-z11 and CEERS_1019 analogues. But given the strong constraints from existing data in Trinity, the extra constraint from GN-z11 and CEERS_1019 does not significantly change trinity model results. (5) z = 6–10 quasar luminosity functions will reduce uncertainties in the trinity prediction of the z = 6–10 SMBH mass–galaxy mass relation by up to ∼0.5 dex. These luminosity functions will be available with future telescopes, such as Roman and Euclid.

A Close Binary Lens Revealed by the Microlensing Event Gaia20bof

During the last 25 yr, hundreds of binary stars and planets have been discovered toward the Galactic bulge by microlensing surveys. Thanks to a new generation of large-sky surveys, it is now possible to regularly detect microlensing events across the entire sky. The OMEGA Key Projet at the Las Cumbres Observatory carries out automated follow-up observations of microlensing events alerted by these surveys with the aim of identifying and characterizing exoplanets as well as stellar remnants. In this study, we present the analysis of the binary lens event Gaia20bof. By automatically requesting additional observations, the OMEGA Key Project obtained dense time coverage of an anomaly near the peak of the event, allowing characterization of the lensing system. The observed anomaly in the lightcurve is due to a binary lens. However, several models can explain the observations. Spectroscopic observations indicate that the source is located at ≤2.0 kpc, in agreement with the parallax measurements from Gaia. While the models are currently degenerate, future observations, especially the Gaia astrometric time series as well as high-resolution imaging, will provide extra constraints to distinguish between them.

Further study on k-restricted edge connectivity and exact k-restricted edge connectivity of a graph

Inspired by the studies on conditional connectivity by Harary [1], we worked on [Formula: see text]-restricted edge connectivity of a graph [Formula: see text] [4]. The [Formula: see text]-restricted edge connectivity of a graph [Formula: see text] is the cardinality of a minimum edge-cut whose deletion disconnects the graph [Formula: see text] into components where each component has order at least [Formula: see text]. In this work, we take into account some results on [Formula: see text]-restricted edge connectivity and the novel parameter exact [Formula: see text]-restricted edge connectivity. In the definition of [Formula: see text]-restricted edge connectivity, we impose some extra constraints to achieve this parameter. In this paper, we consider some fundamental aspects of exact [Formula: see text]-restricted edge connectivity and how they relate to the [Formula: see text]-restricted edge connectivity.

BSEC Method for Unveiling Open Clusters and its Application to Gaia DR3: 83 New Clusters

Open clusters (OCs) are common in the Milky Way, but most of them remain undiscovered. There are numerous techniques, including some machine-learning algorithms, available for the exploration of OCs. However, each method has its limitations and therefore, different approaches to discovering OCs hold significant values. We develop a comprehensive approach method to automatically explore the data space and identify potential OC candidates with relatively reliable membership determination. This approach combines the techniques of Hierarchical Density-Based Spatial Clustering of Applications with Noise, Gaussian mixture model, and a novel cluster member identification technique, color excess constraint. The new method exhibits efficiency in detecting OCs while ensuring precise determination of cluster memberships. Because the main feature of this technique is to add an extra constraint (EC) for the members of cluster candidates using the homogeneity of color excess, compared to typical blind search codes, it is called Blind Search-Extra Constraint (BSEC) method. It is successfully applied to the Gaia Data Release 3, and 83 new OCs are found, whose color–magnitude diagrams (CMDs) are fitted well to the isochrones. In addition, this study reports 621 new OC candidates with discernible main sequence or red giant branch. It is shown that BSEC technique can discard some false negatives of previous works, which takes about three percentage of known clusters. It shows that as an EC, the color excess (or two-color) constraint is useful for removing fake cluster member stars from the clusters that are identified from the positions and proper motions of stars, and getting more precise CMDs, when differential reddening of member stars of a cluster is not large (e.g., ΔE(G BP − G RP) < 0.5 mag). It makes the CMDs of 15% clusters clearer (in particular for the region near turnoff) and therefore is helpful for CMD and stellar population studies. Our result suggests that the color excess constraint is more appropriate for clusters with small differential reddening, such as globular clusters or older OCs, and clusters that the distances of member stars cannot be determined accurately.

Finite element implementation of Field Crack Mechanics for brittle and ductile fracture

In this work, a Finite Element (FE) implementation of a Field Crack Mechanics (FCM) model is presented for the first time. The implementation includes general boundary conditions and application to bulk plasticity as well. The current numerical investigation adopts the standard Galerkin finite element formulation to solve the equation of linear momentum balance and finite difference framework for crack evolution. Our preliminary investigation includes the modes-I and II loading conditions, where their respective normal stress fields are compared against their analytical counterparts. The fundamental questions in classical fracture mechanics, e.g. the existence of threshold stress for the crack to move, and various stages associated with the crack propagation are investigated. Additionally, this study explores two distinct strain energy functions based on the crack surface normal and hydrostatic deviatoric energy split. Crack irreversibility is a natural phenomenon in the FCM model, and it does not require satisfying any extra irreversibility constraints. The model shows good agreement against literature and analytical framework. The current FCM implementation also recovers the basic notion of fracture propagation which satisfies both energy and stress criterion. The study also explores the crack motion under the effect of plasticity in ductile materials. The results thus obtained for both brittle and ductile fracture cases are consistent with the predictions of classical fracture mechanics. The current implementation of the FCM effectively demonstrates stable crack propagation, eliminating the requirement for surfing boundary conditions.

Non-compatible fully [formula omitted] symmetric Davey–Stewartson system: Localized excitation and folded solitary wave

This paper studies a non-compatible fully PT symmetric Davey–Stewartson system which models the evolution of optical wave packet in nonlinear optics. “Non-compatible” means the first two equations of the system are inconsistent that do not need to comply with extra constraint like the compatible case. We employ the multi-linear variable separation approach to derive variable separation solution for this system. The obtained solutions contain four separated free functions, render enough freedom for us to generate diverse solitons. Firstly, we construct two kinds of localized excitations: lump-lattice and periodic-lattice structure. Secondly, we obtain four typical folded solitary waves, i.e. worm-dromion shaped, fin shaped and octopus shaped waves, by introducing suitable multi-valued functions. Lastly, we systematically analyze the interaction between two and three foldons, and give the classification of it. To our knowledge, this is the first time variable separation solution been reported in PT symmetric system. The basic idea of separating variables that used in this paper can be extended to other symmetric systems.