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Machine Learning for Optimization-Based Separation of Mixed-Integer Rounding Cuts
Get PDFMixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then rounding coefficients, but finding the strongest MIR cuts requires optimizing a costly MIP for the aggregation step, so in practice, heuristic strategies for separating fractional points are employed. We propose to improve MIR cut generation in the context of a common scenario in applications, where constraints remain fixed but costs are varied. We present a hybrid cut generation framework in which we train a machine learning (ML) model to classify which constraints are involved in useful MIR cuts based on fractional points from relaxations of the problem. At test time, the predictions of the ML model create a reduced MIP-based generator of MIR cuts. In our experiments, we create an instance family from each of three benchmark MIP instances by performing a careful and costly perturbation of objective coefficients to build a dataset of 1,000 fractional points to be separated over the same constraint set. The results indicate that the reduced separator better strengthens the bound in each round of cut generation, particularly for instances in which the full separator failed to find strong cuts
On the alternatives to the ideal mathematical points-like separatedness
Get PDFIn a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a non-classical logic, in particular the fuzzy sets theory, with events represented as spatiotemporally blurred blobs. Here we point out and discuss a number of aspects of this imperfect symbolic description that might potentially be misleading. Besides that, we analyze its relation to various concepts used commonly to model physical systems, denoted by terms like: point, set, continuous, discrete, infinite, or local, clarifying further how our viewpoint is different and asking whether, in light of our main postulate, any of these notions, or their opposites, if exist, are in their usual meanings suitable to accurately describe the natural phenomena.12 pages, 1 figure; added references, refined argumentatio
Interacting dark sector from Horndeski theories and beyond: Mapping fields and fluids
No full textIn Cosmology, when dissipative effects are minimal, the energy content of the Universe can be effectively described as a sum of perfect fluids. Perfect fluid descriptions ensure thermal equilibrium since they equilibrate immediately. However, interactions among different energy content of the Universe might prevent such rapid equilibration. This limitation calls for a more fundamental framework that incorporates these interactions directly at the level of the action. In earlier work, two of the authors demonstrated that an interacting dark energy (DE)-dark matter (DM) field theory action could be derived from a modified gravity action via a conformal transformation, establishing a one-to-one correspondence between the field theory action and fluid for a unique interaction term [arXiv:2006.04618]. In this work, we extend that analysis by considering quadratic order Horndeski gravity, identifying two classes of models: field coupling and field-kinetic coupling. Our approach generalizes the coupling function for DE-DM interactions by incorporating an additional dependence on kinetic terms. We establish a field-to-fluid mapping for dark matter and find that this mapping only holds for a specific form of the interaction strength. Interestingly, we show that this interaction strength excludes non-gravitational interactions between dark energy and dark radiation. Numerical analysis reveals that purely kinetic interactions within the dark sector can significantly alter cosmological evolution compared to non-interacting scenarios, highlighting the strong dependence of cosmological dynamics on coupling strength. A preliminary examination of linear scalar perturbations indicates that the field-kinetic coupling results in a non-zero gravitational slip parameter and momentum exchange.Version accepted for publication in Physical Review D, added a section in the appendix, slight modification to figures and tables. 52 pages, 15 figures, 3 table
Disturbance-Robust Backup Control Barrier Functions: Safety Under Uncertain Dynamics
No full textObtaining a controlled invariant set is crucial for safety-critical control with control barrier functions (CBFs) but is non-trivial for complex nonlinear systems and constraints. Backup control barrier functions allow such sets to be constructed online in a computationally tractable manner by examining the evolution (or flow) of the system under a known backup control law. However, for systems with unmodeled disturbances, this flow cannot be directly computed, making the current methods inadequate for assuring safety in these scenarios. To address this gap, we leverage bounds on the nominal and disturbed flow to compute a forward invariant set online by ensuring safety of an expanding norm ball tube centered around the nominal system evolution. We prove that this set results in robust control constraints which guarantee safety of the disturbed system via our Disturbance-Robust Backup Control Barrier Function (DR-bCBF) solution. The efficacy of the proposed framework is demonstrated in simulation, applied to a double integrator problem and a rigid body spacecraft rotation problem with rate constraints.Accepted for publication in IEEE Control Systems Letters (L-CSS). 6 pages, 4 figure
Plasmonic Metal Oxide Nanocrystals as Building Blocks for Infrared Metasurfaces
No full textBased on experimental and simulation methods we helped develop, we are advancing mechanistic understanding of how self-assembled NC metamaterials can produce distinctive near- and far-field optical properties not readily achievable in lithographically patterned structures. First, the impacts of the inevitable defects and disorder associated with self-assembly can be rationalized and, in some cases, recognized as advantageous. Second, self-assembly enables intimate nanoscale intermixing of different NC and molecular components. By incorporating probe molecules within the gaps between NCs where the electric field enhancement is strongest, we show enhanced detection of molecular vibrations that can be optimized by tuning the size and resonance frequency of the NCs. We show how metasurfaces incorporating mixtures of NCs with different doping concentrations can achieve epsilon-near-zero dielectric response over a broad frequency range. Finally, considering the NC metasurface itself as a building block, we show how photonic structures incorporating these assemblies can harness and amplify their distinctive properties. Through modeling the NC monolayer as a slab with an effective permittivity response, we designed a frequency-tunable IR perfect absorber by layering the NCs on a simple open cavity structure. Since the perfect absorption architecture further enhances the IR electric field localization strength, we expect that this integration strategy can enhance molecular vibration coupling or non-linear optical response. The versatility of the NC assembly and integration approach suggests opportunities for various metal oxide NC superstructures, including mixing and stacking of NCs beyond a single monolayer, representing a vast parameter space for design of linear and nonlinear IR optical components.33 pages, 5 figure
See Where You Read with Eye Gaze Tracking and Large Language Model
No full textLosing track of reading progress during line switching can be frustrating. Eye gaze tracking technology offers a potential solution by highlighting read paragraphs, aiding users in avoiding wrong line switches. However, the gap between gaze tracking accuracy (2-3 cm) and text line spacing (3-5 mm) makes direct application impractical. Existing methods leverage the linear reading pattern but fail during jump reading. This paper presents a reading tracking and highlighting system that supports both linear and jump reading. Based on experimental insights from the gaze nature study of 16 users, two gaze error models are designed to enable both jump reading detection and relocation. The system further leverages the large language model\u27s contextual perception capability in aiding reading tracking. A reading tracking domain-specific line-gaze alignment opportunity is also exploited to enable dynamic and frequent calibration of the gaze results. Controlled experiments demonstrate reliable linear reading tracking, as well as 84% accuracy in tracking jump reading. Furthermore, real field tests with 18 volunteers demonstrated the system\u27s effectiveness in tracking and highlighting read paragraphs, improving reading efficiency, and enhancing user experience.9 page
CAS-GAN for Contrast-free Angiography Synthesis
Get PDFIodinated contrast agents are widely utilized in numerous interventional procedures, yet posing substantial health risks to patients. This paper presents CAS-GAN, a novel GAN framework that serves as a virtual contrast agent to synthesize X-ray angiographies via disentanglement representation learning and vessel semantic guidance, thereby reducing the reliance on iodinated contrast agents during interventional procedures. Specifically, our approach disentangles X-ray angiographies into background and vessel components, leveraging medical prior knowledge. A specialized predictor then learns to map the interrelationships between these components. Additionally, a vessel semantic-guided generator and a corresponding loss function are introduced to enhance the visual fidelity of generated images. Experimental results on the XCAD dataset demonstrate the state-of-the-art performance of our CAS-GAN, achieving a FID of 5.87 and a MMD of 0.016. These promising results highlight CAS-GAN\u27s potential for clinical applications.IEEE Symposium Series on Computational Intelligence (SSCI 2025
Inferentially-Private Private Information
No full textInformation disclosure can compromise privacy when revealed information is correlated with private information. We consider the notion of inferential privacy, which measures privacy leakage by bounding the inferential power a Bayesian adversary can gain by observing a released signal. Our goal is to devise an inferentially-private private information structure that maximizes the informativeness of the released signal, following the Blackwell ordering principle, while adhering to inferential privacy constraints. To achieve this, we devise an efficient release mechanism that achieves the inferentially-private Blackwell optimal private information structure for the setting where the private information is binary. Additionally, we propose a programming approach to compute the optimal structure for general cases given the utility function. The design of our mechanisms builds on our geometric characterization of the Blackwell-optimal disclosure mechanisms under privacy constraints, which may be of independent interest
Enhancement of adhesion strength through microvibrations: modeling and experiments
No full textHigh-frequency micrometrical vibrations have been shown to greatly influence the adhesive performance of soft interfaces, however a detailed comparison between theoretical predictions and experimental results is still missing. Here, the problem of a rigid spherical indenter, hung on a soft spring, that is unloaded from an adhesive viscoelastic vibrating substrate is considered. The experimental tests were performed by unloading a borosilicate glass lens from a soft PDMS substrate excited by high-frequency micrometrical vibrations. We show that as soon as the vibration starts, the contact area increases abruptly and during unloading it decreases following approximately the JKR classical model, but with a much increased work of adhesion. We find that the pull-off force increases with respect to the amplitude of vibration up to a certain saturation level, which appeared to be frequency dependent. Under the hypothesis of short range adhesion, a lumped mechanical model was derived, which, starting from an independent characterization of the rate-dependent interfacial adhesion, predicted qualitatively and quantitatively the experimental results, without the need of any adjustable parameters
Listing 6-Cycles in Sparse Graphs
Get PDFThis work considers the problem of output-sensitive listing of occurrences of -cycles for fixed constant in an undirected host graph with edges and -cycles. Recent work of Jin and Xu (and independently Abboud, Khoury, Leibowitz, and Safier) [STOC 2023] gives an time algorithm for listing -cycles, and recent work by Jin, Vassilevska Williams and Zhou [SOSA 2024] gives an time algorithm for listing -cycles in node graphs. We focus on resolving the next natural question: obtaining listing algorithms for -cycles in the sparse setting, i.e., in terms of rather than . Previously, the best known result here is the better of Jin, Vassilevska Williams and Zhou\u27s algorithm and Alon, Yuster and Zwick\u27s algorithm.
We give an algorithm for listing -cycles with running time . Our algorithm is a natural extension of Dahlgaard, Knudsen and Stöckel\u27s [STOC 2017] algorithm for detecting a -cycle. Our main technical contribution is the analysis of the algorithm which involves a type of ``supersaturation\u27\u27 lemma relating the number of -cycles in a bipartite graph to the sizes of the parts in the bipartition and the number of edges. We also give a simplified analysis of Dahlgaard, Knudsen and Stöckel\u27s -cycle detection algorithm (with a small polylogarithmic increase in the running time), which is helpful in analyzing our listing algorithm.19 page