Narrow Results

A counterterrorism model is developed where a government and a terrorist allocate resources over two periods. Escalation to period 2 occurs if a threshold for the government’s period-1 damage is exceeded. Without escalation four scenarios exist, including deterrence and nonprovocation. With escalation and unitary contest intensity, both players’ fractions of their resources allocated to period 1 equal the sum of their potential period-1 damages divided by the sum of their potential damages in both periods. As the government’s resource superiority increases, the terrorist allocates all its resources to the period-1 attack, and the government deters escalation. Uniform distributions of the contest intensity and the government’s resource superiority over various intervals are considered. Observing that the terrorist’s utility may be U-shaped in the escalation threshold, the government is enabled to determine both its resource allocation and escalation threshold. The government prefers no threshold when it lacks resources and should always escalate, and when it has abundant resources and can deter. For intermediate resource superiority, the government prefers an intermediate threshold. Six game outcomes are shown where escalation is deterred for two disjoint intervals of the government’s resource superiority.

In this paper we prove that the four-point function of massive -theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.

We consider the one-dimensional discrete Schrödinger operator on ℤ, and study the relation between the generalized eigenstates and the asymptotic expansion of the resolvent for the threshold 0. We decompose the generalized zero eigenspace into subspaces, some of which correspond to the bound states or the resonance states, only by their growth properties at infinity, and precisely describe the first few leading coefficients in the expansion using these subspaces. The generalized zero eigenspace we consider is the largest possible one, consisting of all solutions to the eigenequation. For the resolvent expansion, we implement the expansion scheme of Jensen–Nenciu [Rev. Math. Phys.13 (2001) 717–754] and [Rev. Math. Phys.16 (2004) 675–677] in its full generality.

Changes in heart rate, most often increases, are associated with the onset of epileptic seizures and may be used in lieu of cortical activity for automated seizure detection. The feasibility of this aim was tested on 241 clinical seizures from 81 subjects admitted to several Epilepsy Centers for invasive monitoring for evaluation for epilepsy surgery. The performance of the EKG-based seizure detection algorithm was compared to that of a validated algorithm applied to electrocorticogram (ECoG). With the most sensitive detection settings [threshold T: 1.15; duration D: 0 s], 5/241 seizures (2%) were undetected (false negatives) and with the highest [T: 1.3; D: 5 s] settings, the number of false negative detections rose to 34 (14%). The rate of potential false positive (PFP) detections was 9.5/h with the lowest and 1.1/h with the highest T, D settings. Visual review of 336 ECoG segments associated with PFPs revealed that 120 (36%) were associated with seizures, 127 (38%) with bursts of epileptiform discharges and only 87 (26%) were true false positives. Electrocardiographic (EKG)-based seizure onset detection preceded clinical onset by 0.8 s with the lowest and followed it by 13.8 s with the highest T, D settings. Automated EKG-based seizure detection is feasible and has potential clinical utility given its ease of acquisition, processing, high signal/noise and ergonomic advantages viz-a-viz EEG (electroencephalogram) or ECoG. Its use as an "electronic" seizure diary will remedy in part, the inaccuracies of those generated by patients/care-givers in a cost-effective manner.

The development of social networks provides a broad platform for the dissemination of information and also leads to the proliferation of fake news and false information, which we collectively refer to as rumors. The spread of rumors causes unnecessary panic and loss to individuals and society. To reduce the negative impacts of rumors, an appropriate rumor control strategy is necessary. To come up with some reasonable strategies, we need to have a clearer understanding of the spread of rumors. In this paper, we analyze crowd attitudes during the spreading of rumors by setting the misinformation prevalent progress on the social network as a dynamic system. Considering that most people do not have a clear supportive or opposing attitude when exposed to rumor information, we introduce a new group, stiflers who remain neutral, based on the infectious disease model scheme. By deriving the mean-field equation describing the rumor propagation process, we judge the stability of the constructed model. Finally, we use the model to fit the real-world data related to COVID-19, and based on this, we discuss the properties of the model and propose related strategies.

The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we find p_c=0.311605(5) in the cubic lattice.

This paper evaluates the impact of demographic change on the economic growth of OECD and non-OECD countries. An annual panel dataset of 71 countries, consisting of 27 advanced economies and 44 emerging economies over the period of 1981–2014, is used. Two types of regression models (panel regression model and panel continuous threshold model) including several demographic variables are used to investigate the effects of demographic structure. The results of this study show the significant difference of the impact of demographic transition on the economic growth of OECD and non-OECD economies.

This paper investigates the threshold effects of population aging on economic growth using country-level panel data covering 98 countries from 1970 to 2015. The overall estimation results indicate significant nonlinear effects on economic growth of the share of the elderly in the total population, with the estimated threshold between 10.1% and 10.9%. Beyond the threshold, deeper population aging begins to have negative effects on economic growth. Second, most of the threshold effects comes from the group of non-OECD countries, i.e., low-income countries, while the insignificant and delayed threshold effects are found in OECD countries, i.e., high- and middle-income countries. Third, as net capital inflows grow, particularly by the debt type, they can increase long-run economic growth in OECD countries, while they overall cause to deteriorate it in non-OECD countries. And finally, for the OECD countries, the positive impacts of capital inflows on growth are partially cancelled out as heightening in degree of population aging. These findings are overall robust to alternative measure of population aging, old-age dependency ratio and alternative country groups such as using US$7,000 in GDP per capita 1990 as reference income level. These results suggest that sufficient human capital investment, adoption of high technologies, and development of economic institutions including financial and foreign exchange markets are recommended in response to upcoming negative effects of population aging on economic growth especially for low-income country.

We consider a multi-server queueing model in which arrivals occur according to a Markovian arrival process (MAP). There is a single-server and additional (backup) servers are added or removed depending on sets of thresholds. The service times are assumed to be exponential and the servers are assumed to be homogeneous. A comparison of this model to the classical MAP/M/c queueing model through an optimization problem yields some interesting results that are useful in practical applications. For example, we notice that positively correlated arrival process appears to benefit with the threshold type queueing model. We also give the minimum delay costs and the associated maximum setup costs so that the threshold type queueing model is to be preferred over the classical MAP/M/c model.

We use the theory of YFS resummation to compute the size of the expected resummed soft radiative threshold effects in precision studies of heavy particle production at the LHC, where accuracies of 1% are desired in some processes. We find that the soft QED threshold effects are at the level of 0.3% whereas the soft QCD threshold effects enter at the level of 20% and hence both must be controlled to be on the conservative side to achieve such goals.

Threshold behavior of the cross-sections of ultraperipheral nuclear interactions is studied. Production of $e^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{-}$ pairs as well as ${\pi }^0$ and parapositronium is treated. The values of corresponding energy thresholds are presented and the total cross-sections of these processes at the newly constructed NICA and FAIR facilities are estimated.

We review some results on the phenomenology of networks of chaotic elements under threshold activated coupling. We show how thresholding at different levels gives rise to behaviour ranging from spatiotemporal cycles and spatiotemporal chaos, to scaling regimes reminiscent of self-organized criticality. We also indicate how our knowledge of the dynamical consequences of varying threshold levels can be used to design control algorithms targetting a wide range of spatiotemporal patterns. Some of these concepts are verified in experiments on chaotic electrical circuits.

In this paper, the neuronal firing patterns under extracellular sinusoidal electric field (EF) are investigated based on a reduced two-compartment model with focus on the effects of morphological and internal coupling parameters. We observe that the neuron can exhibit bursting, synchronous firing and subthreshold oscillation depending on EF amplitude A and frequency f. Furthermore, neuronal firing properties change obviously over a range of morphological parameter p. As p increases, the firing region expands first and then diminishes gradually until it disappears in the observed (A, f) parameter space and the transition from bursting to synchronous firing is also markedly distinct. Meanwhile, the morphological parameter also has significant effects on the EF threshold for triggering neuronal spikes. Unlike morphological parameter, though the internal coupling conductance g_c can also induce some changes in firing behavior and EF threshold, it cannot qualitatively change neuronal dynamical properties. All these results demonstrate that neuronal morphology plays a crucial role in neuronal responses to sinusoidal EF.

In order to study the forming mechanism of metal jet under electromagnetic loading, numerical simulation for electromagnetic coupled jet forming was realized by using AUTODYN software with secondary development. Through secondary development, the magnetic pressure on the liner during the collapse process is calculated iteratively, which enables numerical simulation for electromagnetically coupled jets. The influence and threshold condition of electromagnetic parameters for jet forming are obtained through this. The results show that the head velocity and length of the jet are improved for liner without a tip. The electromagnetic parameters and structural parameters need to match with each other. The head velocity and effective length of the jet increase with the increase in wall thickness and cone angle. The liner diameter has little effect on the head velocity and effective length of the jet. The head velocity and effective length of the jet first increase and then decrease with the increase in cone radius.

This paper describes a standard cell-based new approach of comparator design for flash ADC. Conventional flash ADC comparator consumes up to 60% of the power due to resistive ladder network and analog comparators. Threshold inverter quantized (TIQ) comparators reported earlier have improved speed and provide low-power, low-voltage operation. But they need feature size variation and have non-linearity issues. Here, a new standard cell comparator is proposed which retains all advantages of TIQ comparator and provides improved linearity with reduced hardware complexity. A 4-bit ADC designed using the proposed comparator requires 206 minimum-sized transistors and provides large area saving compared to previously proposed designs. Thermometer code is partitioned using algebraic division theorem. This conversion is used for mathematical modeling and complexity reduction of decoder circuit using semi-parallel organization of comparators. Circuit is designed using 90 nm technology which exhibits satisfactory performance even in process variation.

A nonlinear recurrence involving a piecewise constant McCulloch–Pitts function and two 2-periodic coefficient sequences is investigated. By allowing the threshold parameter to vary from 0⁺ to +∞, we work out a complete bifurcation analysis for the asymptotic behaviors of the corresponding solutions. We show that there are four steady state solutions and that all solutions will tend to one of them. We hope that our results will be useful in further investigating neural networks involving the McCulloch–Pitts function with threshold and more general periodic coefficients.

The negative or hyperpolarization pulse stimulation induces action potential, i.e. the post-inhibitory rebound spike, which has been widely observed in various single neurons with hyperpolarization-activated cation current ($I_{\mathrm{\text{h}}}$) in neuroscience and is suggested to be evoked from a focus near the Hopf bifurcation according to the traditional viewpoint of nonlinear dynamics. In the present paper, a novel viewpoint that post-inhibitory rebound spike can be evoked from a stable node near the saddle-node bifurcation on invariant circle (SNIC) is proposed, which can be well interpreted with hyperpolarization activation characteristic of $I_{\mathrm{\text{h}}}$ current, bifurcation analysis, and threshold. Especially, the boundary between the subthreshold and suprathreshold initial values which respectively evoke subthreshold potential and action potential is acquired to be a threshold surface containing the saddle. $I_{\mathrm{\text{h}}}$ current after the negative pulse stimulation for small conductance $g_{\mathrm{\text{h}}}$ of $I_{\mathrm{\text{h}}}$ is low enough to evoke just a subthreshold potential while for large $g_{\mathrm{\text{h}}}$ is high enough to evoke a post-inhibitory rebound spike. For small $g_{\mathrm{\text{h}}}$, the pulse induces the decrease of membrane potential $V$ and then the phase trajectory always stays within the subthreshold initial value region locating lower to the threshold surface with a nearly fixed $V$ value. For large $g_{\mathrm{\text{h}}}$, the threshold surface changes and is composed of two parts: one part with a nearly fixed $V$ value and the other with a nearly fixed value of $H$ variable to describe $I_{\mathrm{\text{h}}}$ inactivation probability. Although the negative pulse stimulation induces the decrease of $V$, $H$ increases to a level high enough and then the phase trajectory runs across the part with a nearly fixed $H$ value to form a post-inhibitory rebound spike. The appearance of the novel $H$ threshold is the internal dynamical mechanism for the generation of post-inhibitory rebound spike, and the external cause is that the negative pulse stimulation induces the phase trajectory to run across the $H$ threshold surface. The results present a novel nonlinear phenomenon and the corresponding dynamical mechanism related to post-inhibitory rebound spike induced by $I_{\mathrm{\text{h}}}$ current near the SNIC bifurcation point.

In this article, we consider a SIV infectious disease control system with two-threshold guidance, in which infection rate and vaccination rate are represented by a piecewise threshold function. We analyze the global dynamics of the discontinuous system using the theory of differential equations with discontinuous right-hand sides. We find some dynamical behaviors, including the disease-free equilibrium and endemic equilibria of three subsystems, a globally asymptotically stable pseudo-equilibrium and two endemic equilibria bistable, one of the two pseudo-equilibria or pseudo-attractor is stable. Conclusions can be used to guide the selection of the most appropriate threshold and parameters to achieve the best control effect under different conditions. We hope to minimize the scale of the infection so that the system can eventually stabilize at the disease-free equilibrium, pseudo-equilibrium or pseudo-attractor, corresponding to the disease disappearing or becoming endemic to a minimum extent, respectively.

Many studies have explored the methods of deriving thresholds of object-oriented (i.e. OO) metrics. Unsupervised methods are mainly based on the distributions of metric values, while supervised methods principally rest on the relationships between metric values and defect-proneness of classes. The objective of this study is to empirically examine whether there are effective threshold values of OO metrics by analyzing existing threshold derivation methods with a large-scale meta-analysis. Based on five representative threshold derivation methods (i.e. VARL, ROC, BPP, MFM, and MGM) and 3268 releases from 65 Java projects, we first employ statistical meta-analysis and sensitivity analysis techniques to derive thresholds for 62 OO metrics on the training data. Then, we investigate the predictive performance of five candidate thresholds for each metric on the validation data to explore which of these candidate thresholds can be served as the threshold. Finally, we evaluate their predictive performance on the test data. The experimental results show that 26 of 62 metrics have the threshold effect and the derived thresholds by meta-analysis achieve promising results of GM values and significantly outperform almost all five representative (baseline) thresholds.

With the rapid growth of microarray data, it has become a hot topic to reveal complex behaviors and functions of life system by studying the relationships among genes. In the process of reverse network modeling, the relationships with less relevance are generally not considered by determining a threshold when the relationships among genes are mined. However, there are no effective methods to determine the threshold up to now. It is worthwhile to note that the phenotypes of genetic diseases are generally regarded as external representation of the functions of genes. Therefore, two types of phenotype networks are constructed from gene and disease views, respectively, and through comparing these two types of phenotype networks, the threshold of gene network corresponding to a certain disease can be determined when their similarity reaches to maximum. Because the gene network is determined based on the relationships among phenotypes and phenotypes are external representation of the functions of genes, it is considered that relationships in the gene network may show functional relationships among genes in biological system. In this work, the thresholds 0.47 and 0.48 of gene network are determined based on Parkinson disease phenotypes. Furthermore, the validity of these thresholds is verified by the specificity and susceptibility of phenotype networks. Also, through comparing the structural parameters of gene networks for normal and disease stage at different thresholds, significant difference between the two gene networks at threshold 0.47 or 0.48 is found. The significant difference of structural parameters further verifies the efficiency of this method.