Miracle-dz/UniFAR-FTUs huggingface dataset:
Classical KMS Functionals and Phase Transitions in Poisson Geometry

We study the convex cone of not necessarily smooth measures satisfying the classical KMS condition within the context of Poisson geometry. We discuss the general properties of KMS measures and its relation with the underlying Poisson geometry in analogy to Weinstein's seminal work in the smooth case. Moreover, by generalizing results from the symplectic case, we focus on the case of $b$-Poisson manifolds, where we provide an almost complete characterization of the convex cone of KMS measures.
Mutually-aware Sub-Graphs Differentiable Architecture Search

Differentiable architecture search is prevalent in the field of NAS because of its simplicity and efficiency, where two paradigms, multi-path algorithms and single-path methods, are dominated. Multi-path framework (e.g. DARTS) is intuitive but suffers from memory usage and training collapse. Single-path methods (e.g.GDAS and ProxylessNAS) mitigate the memory issue and shrink the gap between searching and evaluation but sacrifice the performance. In this paper, we propose a conceptually simple yet efficient method to bridge these two paradigms, referred as Mutually-aware Sub-Graphs Differentiable Architecture Search (MSG-DAS). The core of our framework is a differentiable Gumbel-TopK sampler that produces multiple mutually exclusive single-path sub-graphs. To alleviate the severer skip-connect issue brought by multiple sub-graphs setting, we propose a Dropblock-Identity module to stabilize the optimization. To make best use of the available models (super-net and sub-graphs), we introduce a memory-efficient super-net guidance distillation to improve training. The proposed framework strikes a balance between flexible memory usage and searching quality. We demonstrate the effectiveness of our methods on ImageNet and CIFAR10, where the searched models show a comparable performance as the most recent approaches.
Flows, growth rates, and the veering polynomial

Abstract For a pseudo-Anosov flow $\varphi $ without perfect fits on a closed $3$ -manifold, Agol–Guéritaud produce a veering triangulation $\tau $ on the manifold M obtained by deleting the singular orbits of $\varphi $ . We show that $\tau $ can be realized in M so that its 2-skeleton is positively transverse to $\varphi $ , and that the combinatorially defined flow graph $\Phi $ embedded in M uniformly codes the orbits of $\varphi $ in a precise sense. Together with these facts, we use a modified version of the veering polynomial, previously introduced by the authors, to compute the growth rates of the closed orbits of $\varphi $ after cutting M along certain transverse surfaces, thereby generalizing the work of McMullen in the fibered setting. These results are new even in the case where the transverse surface represents a class in the boundary of a fibered cone of M. Our work can be used to study the flow $\varphi $ on the original closed manifold. Applications include counting growth rates of closed orbits after cutting along closed transverse surfaces, defining a continuous, convex entropy function on the ‘positive’ cone in $H^1$ of the cut-open manifold, and answering a question of Leininger about the closure of the set of all stretch factors arising as monodromies within a single fibered cone of a $3$ -manifold. This last application connects to the study of endperiodic automorphisms of infinite-type surfaces and the growth rates of their periodic points.
Optimal nonequilibrium thermometry in finite time

What is the minimum time required to take the temperature? In this paper, we solve this question for any process where temperature is inferred by measuring a probe (the thermometer) weakly coupled to the sample of interest, so that the probe’s evolution is well described by a quantum Markovian master equation. Considering the most general control strategy on the probe (adaptive measurements, arbitrary control on the probe’s state and Hamiltonian), we provide bounds on the achievable measurement precision in a finite amount of time, and show that in many scenarios these fundamental limits can be saturated with a relatively simple experiment. We find that for a general class of sample-probe interactions the scaling of the measurement uncertainty is inversely proportional to the time of the process, a shot-noise like behaviour that arises due to the dissipative nature of thermometry. As a side result, we show that the Lamb shift induced by the probe-sample interaction can play a relevant role in thermometry, allowing for finite measurement resolution in the low-temperature regime (more precisely, the measurement uncertainty decays polynomially with the temperature as T → 0, in contrast to the usual exponential decay with T−1). We illustrate these general results for (i) a qubit probe interacting with a bosonic sample, where the role of the Lamb shit is highlighted, and (ii) a collective superradiant coupling between a N -qubit probe and a sample, which enables a quadratic decay with N of the measurement uncertainty.
A Tight Max-Flow Min-Cut Duality Theorem for Non-Linear Multicommodity Flows

The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow problem, which considers flow of a single commodity. We study a multiple commodity generalization of Max-Flow in which flows are composed of real-valued k-vectors through networks with arc capacities formed by regions in \R^k. Given the absence of a clear notion of ordering in the multicommodity case, we define the generalized max flow as the feasible region of all flow values. We define a collection of concepts and operations on flows and cuts in the multicommodity setting. We study the mutual capacity of a set of cuts, defined as the set of flows that can pass through all cuts in the set. We present a method to calculate the mutual capacity of pairs of cuts, and then generalize the same to a method of calculation for arbitrary sets of cuts. We show that the mutual capacity is exactly the set of feasible flows in the network, and hence is equal to the max flow. Furthermore, we present a simple class of the multicommodity max flow problem where computations using this tight duality result could run significantly faster than default brute force computations. We also study more tractable special cases of the multicommodity max flow problem where the objective is to transport a maximum real or integer multiple of a given vector through the network. We devise an augmenting cycle search algorithm that reduces the optimization problem to one with m constraints in at most \R^{(m-n+1)k} space from one that requires mn constraints in \R^{mk} space for a network with n nodes and m edges. We present efficient algorithms that compute eps-approximations to both the ratio and the integer ratio maximum flow problems.
A new constant behind the rotational velocity of galaxies

The present work is devoted to studying the dynamical evolution of galaxies in scalar-Gauss-Bonnet gravity and its relationship with the MOND paradigm. This study is useful for giving meaning to the presence of a new gravitational constant. The stability of dark matter is strongly dependent on matter density. We are interested in calculating the maximum rotational velocity of galaxies. We show that rotating galaxies can be described by a new parameter that depends both on the minimum value of scalar fields and on the effective mass of this field. According to observational data, we have shown that this parameter is a constant.
Model compression as constrained optimization, with application to neural nets. Part V: combining compressions

Model compression is generally performed by using quantization, low-rank approximation or pruning, for which various algorithms have been researched in recent years. One fundamental question is: what types of compression work better for a given model? Or even better: can we improve by combining compressions in a suitable way? We formulate this generally as a problem of optimizing the loss but where the weights are constrained to equal an additive combination of separately compressed parts; and we give an algorithm to learn the corresponding parts' parameters. Experimentally with deep neural nets, we observe that 1) we can find significantly better models in the error-compression space, indicating that different compression types have complementary benefits, and 2) the best type of combination depends exquisitely on the type of neural net. For example, we can compress ResNets and AlexNet using only 1 bit per weight without error degradation at the cost of adding a few floating point weights. However, VGG nets can be better compressed by combining low-rank with a few floating point weights.
Monolithic multigrid for a reduced-quadrature discretization of poroelasticity

Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the potentially strong coupling between unknowns in the system, saddle-point structure, and the need to account for wide ranges of parameter values, including limiting behavior such as incompressible elasticity. This paper was motivated by an attempt to develop monolithic multigrid preconditioners for the discretization developed in [48]; we show here why this is a difficult task and, as a result, we modify the discretization in [48] through the use of a reduced quadrature approximation, yielding a more"solver-friendly"discretization. Local Fourier analysis is used to optimize parameters in the resulting monolithic multigrid method, allowing a fair comparison between the performance and costs of methods based on Vanka and Braess-Sarazin relaxation. Numerical results are presented to validate the LFA predictions and demonstrate efficiency of the algorithms. Finally, a comparison to existing block-factorization preconditioners is also given.
QoS-Aware Load Balancing in Wireless Networks using Clipped Double Q-Learning

In recent years, long-term evolution (LTE) and 5G NR (5th Generation New Radio) technologies have showed great potential to utilize Machine Learning (ML) algorithms in optimizing their operations, both thanks to the availability of fine-grained data from the field, as well as the need arising from growing complexity of networks. The aforementioned complexity sparked mobile operators’ attention as a way to reduce the capital expenditures (CAPEX) and the operational (OPEX) expenditures of their networks through network management automation (NMA). NMA falls under the umbrella of Self-Organizing Networks (SON) in which 3GPP has identified some challenges and opportunities in load balancing mechanisms for the Radio Access Networks (RANs). In the context of machine learning and load balancing, several studies have focused on maximizing the overall network throughput or the resource block utilization (RBU). In this paper, we propose a novel Clipped Double Q-Learning (CDQL)-based load balancing approach considering resource block utilization, latency and the Channel Quality Indicator (CQI). We compare our proposal with a traditional handover algorithm and a resource block utilization based handover mechanism. Simulation results reveal that our scheme is able to improve throughput, latency, jitter and packet loss ratio in comparison to the baseline algorithms.
Stability of a Bose-condensed mixture on a bubble trap

Stability and dynamical behavior of binary Bose-Einstein condensed mixtures trapped on the surface of a rigid spherical shell are investigated in the mean-field level, exploring the miscibility with and without vortex charges, considering repulsive and attractive interactions. In order to compute the critical points for the stability, we follow the Bogoliubov-de Gennes method for the analysis of perturbed solutions, with the constraint that initially the stationary states are in a complete miscible configuration. For the perturbed equal density mixture, of a homogeneous uniform gas and when hidden vorticity is verified, with the species having opposite azimuthal circulation, we consider small perturbation analysis for each unstable mode, providing a complete diagram with the intra- and inter-species interaction role on the stability of the miscible system. Finally, beyond small perturbation analysis, we explore the dynamics of some repulsive and attractive inter-species states by full numerical solutions of the time-dependent Gross-Pitaevskii equation.
Can we replicate real human behaviour using artificial neural networks?

ABSTRACT Agent-based modelling is a powerful tool when simulating human systems, yet when human behaviour cannot be described by simple rules or maximizing one’s own profit, we quickly reach the limits of this methodology. Machine learning has the potential to bridge this gap by providing a link between what people observe and how they act in order to reach their goal. In this paper we use a framework for agent-based modelling that utilizes human values like fairness, conformity and altruism. Using this framework we simulate a public goods game and compare to experimental results. We can report good agreement between simulation and experiment and furthermore find that the presented framework outperforms strict reinforcement learning. Both the framework and the utility function are generic enough that they can be used for arbitrary systems, which makes this method a promising candidate for a foundation of a universal agent-based model.
Field Tuning Beyond the Heat Death of a Charge-Density-Wave Chain

Time-dependent driving of quantum systems has emerged as a powerful tool to engineer exotic phases far from thermal equilibrium; when the drive is periodic this is called Floquet engineering. The presence of many-body interactions can lead to runaway heating, so that generic systems are believed to heat up until they reach a featureless infinite-temperature state. Finding mechanisms to slow down or even avoid this heat death is a major goal—one such mechanism is to drive toward an even distribution of electrons in momentum space. Here we show how such a mechanism avoids the heat death for a charge-density-wave chain in a strong dc electric field; minibands with nontrivial distribution functions develop as the current is prematurely driven to zero. We also show how the field strength tunes between positive, negative, or close-to-infinite effective temperatures for each miniband. These results suggest that nontrivial metastable distribution functions should be realized in the prethermal regime of quantum systems coupled to slow bosonic modes.
Formation of Lead Halide Perovskite Precursors in Solution: Insight from Electronic‐Structure Theory

Understanding the formation of lead halide (LH) perovskite solution precursors is crucial to gain insight into the evolution of these materials to thin films for solar cells. Using density functional theory in conjunction with the polarizable continuum model, 18 complexes with chemical formula PbX 2 M 4 are investigated, where X = Cl, Br, I, and M are common solvent molecules. Through the analysis of structural properties, binding energies, and charge distributions, the role of halogen species and solvent molecules in the formation of LH perovskite precursors is clarified. It is found that interatomic distances are critically affected by the halogen species, whereas the energetic stability is driven by the solvent coordination to the backbones. Regardless of the solvent, lead iodide complexes are more strongly bound than the others. Based on the charge distribution analysis, it is found that all solvent molecules bind covalently with the LH backbones and that PbI and PbBr bonds lose ionicity in solution. The results contribute to clarify the physical properties of LH perovskite solution precursors and offer a valuable starting point for further investigations on their crystalline intermediates.
Gradient-Based Quantification of Epistemic Uncertainty for Deep Object Detectors

The majority of uncertainty quantification methods for deep object detectors are based on the network output, such as sampling strategies like Monte-Carlo dropout or deep ensembles with straight-forward transfers to object detection. Here, we study gradient-based uncertainty features for object detection. We show that they contain information orthogonal to that of common, output-based uncertainty approximation methods. Meta classification and meta regression are used to produce confidence estimates using gradient features and other methods which are applicable to numerous object detection architectures. Our results show that gradient uncertainty itself performs on par with state-of-the-art methods across different detectors and datasets. We find that combined meta classifiers outperform standalone models. This suggests that sampling strategies may be supplemented by gradient-based uncertainty to obtain improved confidences, contributing to the probabilistic reliability of object detectors in down-stream applications.
Extending density matrix embedding: A static two-particle theory

We introduce Extended Density Matrix Embedding Theory (EDMET), a static quantum embedding theory explicitly self-consistent with respect to local two-body physics. This overcomes the biggest practical and conceptual limitation of more traditional one-body embedding methods, namely the lack of screening and treatment of longer-range interactions. This algebraic zero-temperature embedding augments a local interacting cluster model with a minimal number of bosons from a description of the full system correlations via the random phase approximation, and admits an analytic approach to build a self-consistent Coulomb-exchange-correlation kernel. For extended Hubbard models with non-local interactions, this leads to the accurate description of phase transitions, static quantities and dynamics. We also move towards ab initio systems via the Parriser--Parr--Pople model of conjugated coronene derivatives, finding good agreement with experimental optical gaps.
Extremal graphs without exponentially-small bicliques

The Tur\'an problem asks for the largest number of edges in an $n$-vertex graph not containing a fixed forbidden subgraph $F$. We construct a new family of graphs not containing $K_{s,t}$, for $t= C^s$, with $\Omega(n^{2-1/s})$ edges matching the upper bound of K\"ov\'ari, S\'os and Tur\'an.
Strong Coupling and Non-Local Interactions in MoS2 Monolayers Coupled to High-Q Nanocavities

Atomically thin semiconductors can be readily integrated into a wide range of nanophotonic architectures for applications in quantum photonics and novel optoelectronic devices. We report the observation of non-local interactions of free trions, and strong light-matter coupling of localized excitons in pristine hBN/MoS$_2$/hBN heterostructures coupled to single mode (Q $>10^4$) nanocavities. The excellent photonic and excitonic quality of the cavity and hBN encapsulated MoS$_2$ stem from our integrated nanofabrication approach that does not involve etching through the 2D heterostructure, but rather maximizes the local field amplitude within the MoS$_2$ monolayer. We observe a non-monotonic temperature dependence of the cavity-trion interaction strength, consistent with the non-local light-matter interactions in which the free trion diffuse over lengthscales comparable to the cavity mode volume. For an ensemble of localized excitons trapped at defects in the MoS$_2$, we observe strong light-matter coupling with a collective vacuum Rabi energy of $12.9\pm0.8$ meV. Our approach can be generalized to other optically active 2D materials, opening the way towards harnessing novel light-matter interaction regimes for applications in quantum photonics.
Hoechst Is All You Need: Lymphocyte Classification with Deep Learning

Multiplex immunofluorescence and immunohistochemistry benefit patients by allowing cancer pathologists to identify several proteins expressed on the surface of cells, enabling cell classification, better understanding of the tumour micro-environment, more accurate diagnoses, prognoses, and tailored immunotherapy based on the immune status of individual patients. However, they are expensive and time consuming processes which require complex staining and imaging techniques by expert technicians. Hoechst staining is much cheaper and easier to perform, but is not typically used in this case as it binds to DNA rather than to the proteins targeted by immunofluorescent techniques, and it was not previously thought possible to differentiate cells expressing these proteins based only on DNA morphology. In this work we show otherwise, training a deep convolutional neural network to identify cells expressing three proteins (T lymphocyte markers CD3 and CD8, and the B lymphocyte marker CD20) with greater than 90% precision and recall, from Hoechst 33342 stained tissue only. Our model learns previously unknown morphological features associated with expression of these proteins which can be used to accurately differentiate lymphocyte subtypes for use in key prognostic metrics such as assessment of immune cell infiltration,and thereby predict and improve patient outcomes without the need for costly multiplex immunofluorescence.
Multi-path Convolutional Neural Networks Efficiently Improve Feature Extraction in Continuous Adventitious Lung Sound Detection

We previously established a large lung sound database, HF_Lung_V2 (Lung_V2). We trained convolutional-bidirectional gated recurrent unit (CNN-BiGRU) networks for detecting inhalation, exhalation, continuous adventitious sound (CAS) and discontinuous adventitious sound at the recording level on the basis of Lung_V2. However, the performance of CAS detection was poor due to many reasons, one of which is the highly diversified CAS patterns. To make the original CNN-BiGRU model learn the CAS patterns more effectively and not cause too much computing burden, three strategies involving minimal modifications of the network architecture of the CNN layers were investigated: (1) making the CNN layers a bit deeper by using the residual blocks, (2) making the CNN layers a bit wider by increasing the number of CNN kernels, and (3) separating the feature input into multiple paths (the model was denoted by Multi-path CNN-BiGRU). The performance of CAS segment and event detection were evaluated. Results showed that improvement in CAS detection was observed among all the proposed architecture-modified models. The F1 score for CAS event detection of the proposed models increased from 0.445 to 0.491-0.530, which was deemed significant. However, the Multi-path CNN-BiGRU model outperformed the other models in terms of the number of winning titles (five) in total nine evaluation metrics. In addition, the Multi-path CNN-BiGRU model did not cause extra computing burden (0.97-fold inference time) compared to the original CNN-BiGRU model. Conclusively, the Multi-path CNN layers can efficiently improve the effectiveness of feature extraction and subsequently result in better CAS detection.
Distributed Formation Control for Manipulator End Effectors

This article addresses the problem of achieving and maintaining the 2-D/3-D formation shape of networked manipulator end effectors. We first present a distributed formation controller for manipulators whose system parameters are perfectly known. The formation control objective is achieved by assigning virtual springs between end effectors and by adding damping terms at joints, which provides a clear physical interpretation of the proposed solution. Subsequently, we extend it to the case where manipulator kinematic and system parameters are not exactly known. An extra integrator and an adaptive estimator are introduced for gravitational compensation and stabilization, respectively. Simulation results with planar manipulators and with seven degree-of-freedom humanoid manipulator arms are presented to illustrate the effectiveness of the proposed approach.