Lower Bound Research Articles

Global classical solutions to a multidimensional radiation hydrodynamics model with symmetry and large initial data

AbstractAs a first stage to study the global large solutions of the radiation hydrodynamics model with viscosity and thermal conductivity in the high‐dimensional space, we study the problems in high dimensions with some symmetry, such as the spherically or cylindrically symmetric solutions. Specifically, we will study the global classical large solutions to the radiation hydrodynamics model with spherically or cylindrically symmetric initial data. The key point is to obtain the strict positive lower and upper bounds of the density and the lower bound of the temperature . Compared with the Navier–Stokes equations, these estimates in the present paper are more complicated due to the influence of the radiation. To overcome the difficulties caused by the radiation, we construct a pointwise estimate between the radiative heat flux and the temperature by studying the boundary value problem of the corresponding ordinary differential equation. And we consider a general heat conductivity: if ; if . This can be viewed as the first result about the global classical large solutions of the radiation hydrodynamics model with some symmetry in the high‐dimensional space.

On the crossing limit cycles created by a discontinuous piecewise differential system formed by three linear Hamiltonian saddles

We study planar discontinuous piecewise differential systems formed by three linear Hamiltonian saddles separated by the non-regular line Σ = { ( x , y ) ∈ R 2 : ( y = 0 ) ∨ ( x = 0 ∧ y ≥ 0 ) } . We prove that when the linear Hamiltonian saddles are homogeneous they have no limit cycles, and when they are non homogeneous they can have at most three limit cycles having exactly one point on each branch of Σ, and at most one limit cycle having four intersection points on Σ. Moreover we show that they can have at most one limit cycle having four intersection points on Σ and three limit cycles having three intersection points on Σ, simultaneously. Thus we have solved the extension of the 16th Hilbert problem to this class of piecewise differential systems. Furthermore we show that for the three types of combinations of the limit cycles here studied in two of them the upper bound is sharp by providing examples of these systems with the maximum number of possible limit cycles. For the remaining type of limit cycles the upper bound is four and we have examples with three limit cycles. So at this moment it is an open problem to know if the sharp upper bound is either four or three.

The gap phenomenon for conformally related Einstein metrics

AbstractWe determine the submaximal dimensions of the spaces of almost Einstein scales and normal conformal Killing fields for connected conformal manifolds. The results depend on the signature and dimension of the conformally nonflat conformal manifold. In definite signature, these two dimensions are at most and , respectively. In Lorentzian signature, these two dimensions are at most and , respectively. In the remaining signatures, these two dimensions are at most and , respectively. This upper bound is sharp and to realize examples of submaximal dimensions, we first provide them directly in dimension 4. In higher dimensions, we construct the submaximal examples as the (warped) product of the (pseudo)‐Euclidean base of dimension with one of the 4‐dimensional submaximal examples.

Optimizing Distributions for Associated Entropic Vectors via Generative Convolutional Neural Networks.

The complete characterization of the almost-entropic region yields rate regions for network coding problems. However, this characterization is difficult and open. In this paper, we propose a novel algorithm to determine whether an arbitrary vector in the entropy space is entropic or not, by parameterizing and generating probability mass functions by neural networks. Given a target vector, the algorithm minimizes the normalized distance between the target vector and the generated entropic vector by training the neural network. The algorithm reveals the entropic nature of the target vector, and obtains the underlying distribution, accordingly. The proposed algorithm was further implemented with convolutional neural networks, which naturally fit the structure of joint probability mass functions, and accelerate the algorithm with GPUs. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conducted optimizations of the Ingleton score and Ingleton violation index, where a new lower bound of the Ingleton violation index was obtained. An inner bound of the almost-entropic region with four random variables was constructed with the proposed method, presenting the current best inner bound measured by the volume ratio. The potential of a computer-aided approach to construct achievable schemes for network coding problems using the proposed method is discussed.

The effect of the end-number license plate driving restriction on reducing air pollution in China

This study investigates the long-term efficiency of the long-run end-number license plate driving restriction in China, a traffic control policy that is partially aimed at reducing urban air pollution. A difference-in-differences regression is performed on a panel including nine cities that implemented this policy in staggered manner between 2008 and 2013. The results show that overall, this driving restriction does not improve air pollution in policy cities over the long-term. Quantitatively, the city-level air quality index has close-zero statistically insignificant changes by the policy, reaching only 3.9% reduction by 95% confidence interval lower bound of the estimate, translating to welfare gains of only 11.24 USD (70.62 CNY) per person per year, or 0.447 life years per capita. Further analysis with regression discontinuity in time and heterogeneity subgroup analysis illustrates that air pollution may first decrease due to the policy but then bounce back because of the behavioral adaptations of drivers purchasing a second car in cities without simultaneous car purchase restrictions. This shows that need to combine the end-number license plate policy with car purchase restrictions or electric vehicle promotions to achieve effective air pollution reductions over the long-term.

Interplay of freeze-in and freeze-out: Lepton-flavored dark matter and muon colliders

We study a lepton-flavored dark matter model and its signatures at a future muon collider. We focus on the less-explored regime of feeble dark matter interactions, which suppresses the dangerous lepton-flavor-violating processes, gives rise to dark matter freeze-in production, and leads to long-lived particle signatures at colliders. We find that the interplay of dark matter freeze-in and its mediator freeze-out gives rise to an upper bound of around TeV scales on the dark matter mass. The signatures of this model depend on the lifetime of the mediator and can range from generic prompt decays to more exotic long-lived particle signals. In the prompt region, we calculate the signal yield, study useful kinematics cuts, and report tolerable systematics that would allow for a 5σ discovery. In the long-lived region, we calculate the number of charged tracks and displaced lepton signals of our model in different parts of the detector and uncover kinematic features that can be used for background rejection. We show that, unlike in hadron colliders, multiple production channels contribute significantly, which leads to sharply distinct kinematics for electroweakly charged long-lived particle signals. Ultimately, the collider signatures of this lepton-flavored dark matter model are common among models of electroweak-charged new physics, rendering this model a useful and broadly applicable benchmark model for future muon collider studies that can help inform work on detector design and studies of systematics. Published by the American Physical Society 2024

SNN-BERT: Training-efficient Spiking Neural Networks for energy-efficient BERT

Spiking Neural Networks (SNNs) are naturally suited to process sequence tasks such as NLP with low power, due to its brain-inspired spatio-temporal dynamics and spike-driven nature. Current SNNs employ ”repeat coding” that re-enter all input tokens at each timestep, which fails to fully exploit temporal relationships between the tokens and introduces memory overhead. In this work, we align the number of input tokens with the timestep and refer to this input coding as ”individual coding”. To cope with the increase in training time for individual encoded SNNs due to the dramatic increase in timesteps, we design a Bidirectional Parallel Spiking Neuron (BPSN) with following features: First, BPSN supports spike parallel computing and effectively avoids the issue of uninterrupted firing; Second, BPSN excels in handling adaptive sequence length tasks, which is a capability that existing work does not have; Third, the fusion of bidirectional information enhances the temporal information modeling capabilities of SNNs; To validate the effectiveness of our BPSN, we present the SNN-BERT, a deep direct training SNN architecture based on the BERT model in NLP. Compared to prior repeat 4-timestep coding baseline, our method achieves a 6.46× reduction in energy consumption and a significant 16.1% improvement, raising the performance upper bound of the SNN domain on the GLUE dataset to 74.4%. Additionally, our method achieves 3.5× training acceleration and 3.8× training memory optimization. Compared with artificial neural networks of similar architecture, we obtain comparable performance but up to 22.5× energy efficiency. We would provide the codes.

Ocular adverse events associated with platins: a disproportionality analysis of pharmacovigilance data and extensive systematic review of case reports

ABSTRACT Background Anti-cancer drugs, particularly platinum-based chemotherapy drugs, have been showing ocular adverse events (OAEs) in patients undergoing chemotherapy, which is concerning due to the potential impact on patient’s quality of life and the ability to continue effective cancer treatment. Research design and methods A retrospective case/non-case study was conducted using spontaneous reports on OAEs by platins from the FDA Adverse Event Reporting System (FAERS) database. A disproportionality analysis was performed by calculating the Proportional Reporting Ratio (PRR), Reporting Odds Ratio (ROR), and the Information Component (IC) to identify OAE signals for platinum-based chemotherapy drugs. In parallel, a review of case reports for OAEs from platins was conducted by a systematic literature search in PubMed and Google Scholar. Results Using disproportionality analysis, 69 signals were identified for platinum-based chemotherapy drugs and OAEs (carboplatin: 42, oxaliplatin: 16, cisplatin: 11). Choroidal infarction [PRR = 215.1; χ2 = 4527.1; lower bound (LB) ROR = 140.7; IC025 = 5.1] and orbital hemorrhage [PRR = 120.0; χ2 = 300.5; LB ROR = 35.1; IC025 = 1.3] were the strong signals identified for carboplatin. Optic disc hyperemia [PRR = 208.2; χ2 = 742.5; LB ROR = 74.1; IC025 = 2.2] and blindness cortical [PRR = 23.7; χ2 = 382.5; LB ROR = 14.8; IC025 = 3.1] were the signals identified for oxaliplatin and cisplatin, respectively. A total of 32 case reports of OAEs from platinum-based chemotherapy drugs were identified through a systematic search in PubMed and Google Scholar, strengthening the association. Conclusion The study revealed a potential risk of OAEs when using platinum-based chemotherapy drugs as an anticancer medication.

Similarity law of global and local responses of reinforced concrete beams subjected to impact loading

In the experiment of scaled models to dealing with the impact of reinforced concrete large structures, the strain rate hardening effect can lead to significant differences between the dynamic responses of prototype and model. In the present study, this thorny problem is solved by adjusting the impact velocity. Based on the mechanisms of different dynamic responses, the similarity laws for the global and local responses of reinforced concrete beams subjected to impact loading are proposed by considering the strain-rate effect of materials through Buckingham Π-theorem, where constitutive models of different materials are employed for inferring dynamic stress. In dimensional analysis, multiple control factors need to be considered simultaneously, such as the strain-rate effects of steel and concrete, since reinforced concrete components are typical composite structures. The similarity law cannot be unified when considering multiple control factors. In view of this, it is recommended to estimate the dynamic response of reinforced concrete components subjected to impact loading through the upper and lower bounds of similarity law. The upper bound of similarity law is based on the strain-rate effect of concrete, while the lower bound of similarity law is based on the strain-rate effect of steel bar. The numerical models of reinforced concrete beams are established based on the experimental background. The numerical simulations with different scaling factors indicate that the model modified by the lower bound of similarity law can better predict the global response of prototype, while the model modified by the upper bound of similarity law can more accurately predict the local response of prototype. In addition, the influence of dynamic elastic modulus of reinforced concrete on the similarity law is discussed through comparative analysis.

Facile infiltration of polyethyleneimine as a strong CO2 retardant in scalable dual-polymer membranes for H2/CO2 separation

Successful pre-combustion CO2 capture from synthetic gas for H2 production requires effective membrane separation technology. While polymer-based membrane materials offer promising industrial scalability, they generally lack a sufficiently high H2/CO2 selectivity to make this process energy-efficient. In this work, we have designed a scalable dual-polymer blend membrane consisting of sulfonated polyphenylsulfone (sPPSU) and polybenzimidazole (PBI), and then being infiltrated with amine-rich poly(ethyleneimine) (PEI) molecules as effective CO2 retardants to substantially elevate the H2/CO2 selectivity. PEI molecules were infiltrated into the dual-polymer matrix via solution-treatment to crosslink the polymer network and retard CO2 transport using its amine-rich nature. The PEI infiltration dramatically increased the H2/CO2 selectivity of the dual-polymer matrix from 4.6 to up to 59.3 while maintaining a minimum H2 permeability of 2.49 Barrer at a low temperature of 35 °C, which not only surpasses the Robeson upper bound but also places the newly developed membrane among the best-performing polymer-based membranes. More importantly, the solution infiltration of PEI incurs no phase segregation, maintaining the polymer mechanical robustness, which is crucial for industrial scaling. This study offers promising opportunities to develop three-polymer membrane systems for H2/CO2 separation using synergistic polymer blends and CO2-retarding molecules.

The Lower Bound for Number of Hexagons in Strongly Regular Graphs with Parameters λ = 1 and μ = 2

The Lower Bound for Number of Hexagons in Strongly Regular Graphs with Parameters λ = 1 and μ = 2

Finemap-MiXeR: A variational Bayesian approach for genetic finemapping.

Genome-wide association studies (GWAS) implicate broad genomic loci containing clusters of highly correlated genetic variants. Finemapping techniques can select and prioritize variants within each GWAS locus which are more likely to have a functional influence on the trait. Here, we present a novel method, Finemap-MiXeR, for finemapping causal variants from GWAS summary statistics, controlling for correlation among variants due to linkage disequilibrium. Our method is based on a variational Bayesian approach and direct optimization of the Evidence Lower Bound (ELBO) of the likelihood function derived from the MiXeR model. After obtaining the analytical expression for ELBO's gradient, we apply Adaptive Moment Estimation (ADAM) algorithm for optimization, allowing us to obtain the posterior causal probability of each variant. Using these posterior causal probabilities, we validated Finemap-MiXeR across a wide range of scenarios using both synthetic data, and real data on height from the UK Biobank. Comparison of Finemap-MiXeR with two existing methods, FINEMAP and SuSiE RSS, demonstrated similar or improved accuracy. Furthermore, our method is computationally efficient in several aspects. For example, unlike many other methods in the literature, its computational complexity does not increase with the number of true causal variants in a locus and it does not require any matrix inversion operation. The mathematical framework of Finemap-MiXeR is flexible and may also be applied to other problems including cross-trait and cross-ancestry finemapping.

Extreme bandwidths via stochastic self-phase-modulation

We examine the spectral broadening of stochastic laser pulses experiencing self-phase modulation (SPM) in a medium with Kerr nonlinearity. The statistics of extreme bandwidths emerging from such a process is shown to converge, in the large-sample-size limit, to a generalized Poisson distribution whose mean is given by the exponent of the respective extreme-event statistics. In striking contrast to the SPM spectral broadening of deterministic laser pulses, the properties of spectral broadening in stochastic SPM depend not only on the field intensity and the propagation path, but also on the signal-to-noise ratio a of laser pulses and the sample size N. For N >> 1 laser pulses with a high signal-to-noise ratio, the upper bound of SPM-broadened spectra shifts as (lnN/a2)δs, δs being the deterministic SPM bandwidth. The parameter Na=exp(a2/2) is shown to provide an important benchmark, setting a borderline between deterministic and stochastic SPM. These findings offer useful insights into the extreme-event properties of supercontinuum generation.

Hierarchical estimator-based fixed-time and prescribed-time bipartite consensus of multiple Euler-Lagrange systems with a directed signed graph

This article addresses the fixed-time and prescribed-time bipartite consensus problem of Euler-Lagrange systems (ELSs) under a directed sign graph, taking into consideration both the parametric uncertainties and external disturbances. Novel hierarchical control algorithms employing estimator approaches are proposed to tackle the aforementioned challenges. More specifically, the control protocol is first designed to accomplish fixed-time bipartite consensus (Fix-TBC). The settling time obtained by using fixed-time control algorithm is restricted to its upper bound, but it may result in a conservative estimation of the bound. Consequently, it indicates the need for designing another control protocol to address the prescribed-time bipartite consensus (Pre-TBC) problem. By invoking Lyapunov stability theory, some sufficient conditions for achieving fixed-time and prescribed-time bipartite consensus of the ELSs are derived. Numerical examples are ultimately provided to demonstrate results.

Probabilistic Unitary Synthesis with Optimal Accuracy

The purpose of unitary synthesis is to find a gate sequence that optimally approximates a target unitary transformation. A new synthesis approach, called probabilistic synthesis, has been introduced, and its superiority has been demonstrated over traditional deterministic approaches with respect to approximation error and gate length. However, the optimality of current probabilistic synthesis algorithms is unknown. We obtain the tight lower bound on the approximation error obtained by the optimal probabilistic synthesis, which guarantees the sub-optimality of current algorithms. We also show its tight upper bound, which improves and unifies current upper bounds depending on the class of target unitaries. These two bounds reveal the fundamental relationship of approximation error between probabilistic approximation and deterministic approximation of unitary transformations. From a computational point of view, we show that the optimal probability distribution can be computed by the semidefinite program (SDP) we construct. We also construct an efficient probabilistic synthesis algorithm for single-qubit unitaries, rigorously estimate its time complexity, and show that it reduces the approximation error quadratically compared with deterministic algorithms.

Intervals of posets of a zero-divisor graph

Abstract This article is concerned with bounded partially ordered sets P such that for every p ∈ P ∖ {1} there exists q ∈ P ∖ {0} such that 0 is the only lower bound of {p, q}. The posets P such that P ≅ Q if and only if P and Q have isomorphic zero-divisor graphs are completely characterized. In the case of finite posets, this result is generalized by proving that posets with isomorphic zero-divisor graphs form an interval under the partial order given by P ≲ Q if and only if there exists a bijective poset-homomorphism P → Q. In particular, the singleton intervals correspond to the posets that are completely determined by their zero-divisor graphs. These results are obtained by exploring universal and couniversal orderings with respect to posets that have isomorphic zero-divisor graphs.

Optimal Monetary and Transfer Policy in a Liquidity Trap

AbstractOptimal monetary and fiscal policy are jointly analyzed in a heterogeneous two‐agent New Keynesian environment, where fiscal policy is modeled as lump‐sum transfers. Transfer policy does not substitute for forward guidance—as it entails consumption dispersion costs—nor affect its optimal duration. The stay at the zero lower bound is indeed influenced through two offsetting channels: a shortening channel works through an initial increase in transfers that mitigates the recession (reducing the need for forward guidance), while a lengthening channel works through a later transfer cut that curbs the expansion (making forward guidance desirable for a longer horizon).

Distributed predefined-time economic dispatch based on event-triggered strategy for microgrids under directed graphs

The proliferation of new energy solutions and the enhanced accessibility of distributed power sources have significantly increased the complexity and variability of microgrid structures. Due to inherent limitations in its operational mode, the traditional centralized optimization method falls short in effectively addressing the economic dispatch problem in contemporary microgrids. In this paper, a distributed optimization method is devised to address the economic dispatch problem of microgrids under directed graphs by leveraging the consensus algorithm of multi-agent systems. We define the incremental cost of each microgrid unit as the consensus variable, achieving convergence through a pioneering combination of event-triggered strategy and predefined-time control theory. This approach not only optimizes resource use but also ensures timely and efficient solution convergence, addressing critical gaps in existing methodologies. This approach enables control over the upper bound of convergence time for optimal solutions by directly adjusting time parameters in the controller under the directed graph. Consequently, it achieves coordinated control of the power output in microgrids within a predefined time while reducing the communication resources between nodes with event-triggered mechanism. The effectiveness of the proposed algorithm is verified through simulation and analysis.

Classical capacity of quantum non-Gaussian attenuator and amplifier channels

We consider a quantum bosonic channel that couples the input mode via a beam splitter or two-mode squeezer to an environmental mode that is prepared in an arbitrary state. We investigate the classical capacity of this channel, which we call a non-Gaussian attenuator or amplifier channel. If the environment state is thermal, we of course recover a Gaussian phase-covariant channel whose classical capacity is well known. Otherwise, we derive both a lower and an upper bound to the classical capacity of the channel, drawing inspiration from the classical treatment of the capacity of non-Gaussian additive-noise channels. We show that the lower bound to the capacity is always achievable and give examples where the non-Gaussianity of the channel can be exploited so that the communication rate beats the capacity of the Gaussian-equivalent channel (i.e. the channel where the environment state is replaced by a Gaussian state with the same covariance matrix). Finally, our upper bound leads us to formulate and investigate conjectures on the input state that minimizes the output entropy of non-Gaussian attenuator or amplifier channels. Solving these conjectures would be a main step toward accessing the capacity of a large class of non-Gaussian bosonic channels.

Sharp sub-Gaussian upper bounds for subsolutions of Trudinger’s equation on Riemannian manifolds

We consider on Riemannian manifolds the nonlinear evolution equation ∂tu=Δp(u1/(p−1)),where p>1. This equation is also known as a doubly non-linear parabolic equation or Trudinger’s equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including Rn.