In this paper we study how to fairly allocate a set of m indivisible chores to a group of n agents, each of which has a general additive cost function on the items. Since envy-free (EF) allocation is not guaranteed to exist, we consider the notion of
envy-freeness up to any item (EFX). In contrast to the fruitful results regarding the (approximation of) EFX allocations for goods, very little is known for the allocation of chores. Prior to our work, for the allocation of chores, it is known that EFX allocations always exist for two agents, or general number of agents with IDO cost functions. For general instances, no non-trivial approximation result regarding EFX allocation is known. In this paper we make some progress in this direction by showing that for three agents we can always compute a 5-approximation of EFX allocation in polynomial time. For n>=4 agents, our algorithm always computes an allocation that achieves an approximation ratio of O(n^2) regarding EFX.
Understanding electronic properties that violate the Landau Fermi liquid paradigm in cuprate superconductors remains a major challenge in condensed matter physics. The strange metal state in overdoped cuprates that exhibits linear-in-temperature scat
tering rate and dc resistivity is a particularly puzzling example. Here, we compute the electronic scattering rate in the two-dimensional Hubbard model using cluster generalization of dynamical mean-field theory. We present a global phase diagram documenting an apparent non-Fermi liquid phase, in between the pseudogap and Fermi liquid phase in the doped Mott insulator regime. We discover that in this non-Fermi liquid phase, the electronic scattering rate $gamma_k(T)$ can display linear temperature dependence as temperature $T$ goes to zero. In the temperature range that we can access, the $T-$ dependent scattering rate is isotropic on the Fermi surface, in agreement with recent experiments. Using fluctuation diagnostic techniques, we identify antiferromagnetic fluctuations as the physical origin of the $T-$ linear electronic scattering rate.
Mobile edge computing (MEC) is proposed to boost high-efficient and time-sensitive 5G applications. However, the microburst may occur even in lightly-loaded scenarios, which leads to the indeterministic service latency (i.e., unpredictable delay or d
elay variation), hence hindering the deployment of MEC. Deterministic IP networking (DIP) has been proposed that can provide bounds on latency, and high reliability in the large-scale networks. Nevertheless, the direct migration of DIP into the MEC network is non-trivial owing to its original design for the Ethernet with homogeneous devices. Meanwhile, DIP also faces the challenges on the network throughput and scheduling flexibility. In this paper, we delve into the adoption of DIP for the MEC networks and some of the relevant aspects. A deterministic MEC (D-MEC) network is proposed to deliver the deterministic service (i.e., providing the MEC service with bounded service latency). In the D-MEC network, two mechanisms, including the cycle mapping and cycle shifting, are designed to enable: (i) seamless and deterministic transmission with heterogeneous underlaid resources; and (ii) traffic shaping on the edges to improve the resource utilization. We also formulate a joint configuration to maximize the network throughput with deterministic QoS guarantees. Extensive simulations verify that the proposed D-MEC network can achieve a deterministic MEC service, even in the highly-loaded scenarios.
Photoplethysmography (PPG) is a method of detecting variation in blood volume commonly through contact with the skin and involving the usage of one or multiple sensors. PPG is typically used in health-related fields and one of its most popular uses i
s heart rate monitoring. Recent developments in technology have introduced wearable smart devices that can detect PPG signals. These devices mostly rely on signals that are detected at a single location, indicating that such devices require the signal waveform to be immensely reliable. In further detail, the properties of the blood circulation system are being deducted from the heartbeat signal profile. One disadvantage is that the waveform can be affected by tissues that surround the blood vessels. This may result in the unreliability of the methods utilized by many wearable smart devices. This paper introduces an experimental study on the deformation of waveform change caused by sensor binding force. The results of the study are that an increase in sensor binding force decreases the width of the pump strength-related pulse.
We quantify model risk of a financial portfolio whereby a multi-period mean-standard-deviation criterion is used as a selection criterion. In this work, model risk is defined as the loss due to uncertainty of the underlying distribution of the return
s of the assets in the portfolio. The uncertainty is measured by the Kullback-Leibler divergence, i.e., the relative entropy. In the worst case scenario, the optimal robust strategy can be obtained in a semi-analytical form as a solution of a system of nonlinear equations. Several numerical results are presented which allow us to compare the performance of this robust strategy with the optimal non-robust strategy. For illustration, we also quantify the model risk associated with an empirical dataset.
The doubly charmed exotic state $T_{cc}$ recently discovered by the LHCb Collaboration could well be a $DD^{*}$ molecular state long predicted in various theoretical models, in particular, the $DD^*$ isoscalar axial vector molecular state predicted i
n the one-boson-exchange model. In this work, we study the $DDD^*$ system in the Gaussian Expansion Method with the $DD^*$ interaction derived from the one-boson-exchange model and constrained by the precise binding energy of $273pm63$ keV of $T_{cc}$ with respect to the $D^{*+}D^0$ threshold. We show the existence of a $DDD^*$ state with a binding energy of a few hundred keV and spin-parity $1^-$. Its main decay modes are $DDDpi$ and $DDDgamma$. The existence of such a state could in principle be confirmed with the upcoming LHC data and will unambiguously determine the nature of the $T_{cc}^+$ state and of the many exotic state of similar kind, thus deepening our understanding of the non-perturbative strong interaction.
Quantum metrology pursues high-precision measurements to physical quantities by using quantum resources. However, the decoherence generally hinders its performance. Previous work found that the metrology error tends to divergent in the long-encoding-
time regime due to the Born-Markovian approximate decoherence, which is called no-go theorem of noisy quantum metrology. We here propose a Gaussian quantum metrology scheme using bimodal quantized optical fields as quantum probe. It achieves the precision of sub-Heisenberg limit in the ideal case. However, the Markovian decoherence causes the metrological error contributed from the center-of-mass mode of the probe to be divergent. A mechanism to remove this ostensible no-go theorem is found in the non-Markovian dynamics. Our result gives an efficient way to realize high-precision quantum metrology in practical continuous-variable systems.
We report laser cooling and trapping of yttrium monoxide (YO) molecules in an optical lattice. We show that gray molasses cooling remains exceptionally efficient for YO molecules inside the lattice with a molecule temperature as low as 6.1(6) $mu$K.
This approach has produced a trapped sample of 1200 molecules, with a peak spatial density of $sim1.2times10^{10}$ cm$^{-3}$, and a peak phase-space density of $sim3.1times10^{-6}$. By adiabatically ramping down the lattice depth, we cool the molecules further to 1.0(2) $mu$K, twenty times colder than previously reported for laser-cooled molecules in a trap.
We consider the revenue maximization problem in social advertising, where a social network platform owner needs to select seed users for a group of advertisers, each with a payment budget, such that the total expected revenue that the owner gains fro
m the advertisers by propagating their ads in the network is maximized. Previous studies on this problem show that it is intractable and present approximation algorithms. We revisit this problem from a fresh perspective and develop novel efficient approximation algorithms, both under the setting where an exact influence oracle is assumed and under one where this assumption is relaxed. Our approximation ratios significantly improve upon the previous ones. Furthermore, we empirically show, using extensive experiments on four datasets, that our algorithms considerably outperform the existing methods on both the solution quality and computation efficiency.
Optical coherence tomography angiography (OCTA) is a novel non-invasive imaging technique that allows visualizations of vasculature and foveal avascular zone (FAZ) across retinal layers. Clinical researches suggest that the morphology and contour irr
egularity of FAZ are important biomarkers of various ocular pathologies. Therefore, precise segmentation of FAZ has great clinical interest. Also, there is no existing research reporting that FAZ features can improve the performance of deep diagnostic classification networks. In this paper, we propose a novel multi-level boundary shape and distance aware joint learning framework, named BSDA-Net, for FAZ segmentation and diagnostic classification from OCTA images. Two auxiliary branches, namely boundary heatmap regression and signed distance map reconstruction branches, are constructed in addition to the segmentation branch to improve the segmentation performance, resulting in more accurate FAZ contours and fewer outliers. Moreover, both low-level and high-level features from the aforementioned three branches, including shape, size, boundary, and signed directional distance map of FAZ, are fused hierarchically with features from the diagnostic classifier. Through extensive experiments, the proposed BSDA-Net is found to yield state-of-the-art segmentation and classification results on the OCTA-500, OCTAGON, and FAZID datasets.
