The Overshooting Hypothesis of Agricultural Prices: The Role of Asset Substitutability

By allowing for various degrees of asset substitutability between bonds and agricultural products, this paper reexamines the robustness of the overshooting hypothesis of agricultural product prices. It is found, in both a closed economy and an open economy, that the crucial factor determining whether agricultural prices overshoot or undershoot their long-run response following an expansion in the money stock depends upon the extent of asset substitutability between bonds and agricultural goods.asset substitutability, commodity prices, overshooting, Demand and Price Analysis,

Solving the paradox of the folded falling chain by considering horizontal kinetic energy and link geometry

A folded chain, with one end fixed at the ceiling and the other end released from the same elevation, is commonly modeled as an energy-conserving system in one-dimension. However, the analytical paradigms in previous literature is unsatisfying: The theoretical prediction of the tension at the fixed end becomes infinitely large when the free end reaches the bottom, contradicting to the experimental observations. Furthermore, the dependence of the total falling time on the link number demonstrated in numerical simulations is still unexplained. Here, considering the horizontal kinetic energy and the geometry of each link, we derived analytical solutions of the maximal tension as well as the total falling time, in agreement with simulation results and experimental data reported in previous studies. This theoretical perspective shows a simple representation of the complicated two-dimensional falling chain system and, in particular, specifies the signature of the chain properties.Comment: 13 pages, 4 figure

A cusp-capturing PINN for elliptic interface problems

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface. To find such a solution using neural network representation, we introduce a cusp-enforced level set function as an additional feature input to the network to retain the inherent solution properties; that is, capturing the solution cusps (where the derivatives are discontinuous) sharply. In addition, the proposed neural network has the advantage of being mesh-free, so it can easily handle problems in irregular domains. We train the network using the physics-informed framework in which the loss function comprises the residual of the differential equation together with certain interface and boundary conditions. We conduct a series of numerical experiments to demonstrate the effectiveness of the cusp-capturing technique and the accuracy of the present network model. Numerical results show that even using a one-hidden-layer (shallow) network with a moderate number of neurons and sufficient training data points, the present network model can achieve prediction accuracy comparable with traditional methods. Besides, if the solution is discontinuous across the interface, we can simply incorporate an additional supervised learning task for solution jump approximation into the present network without much difficulty

Current Proceedings of Childhood Stroke

Stroke is a sudden onset neurological deficit due to a cerebrovascular event. In children, the recognition of stroke is often delayed due to the low incidence of stroke and the lack of specific assessment measures to this entity. The causes of pediatric stroke are significantly different from that of adult stroke. The lack of safety and efficiency data in the treatment is the challenge while facing children with stroke. Nearly half of survivors of pediatric stroke may have neurologic deficits affecting functional status and quality of life. They may cause a substantial burden on health care resources. Hence, an accurate history, including onset and duration of symptoms, risk factors, and a complete investigation, including hematologic, neuroimaging, and metabolic studies is the key to make a corrective diagnosis. A prompt and optimal treatment without delay may minimize the damage to the brain

An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications

A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across the interface, when applying finite difference discretization to this problem, an additional treatment accounting for the jump discontinuities must be employed. Here, we aim to elevate such an extra effort to ease our implementation by machine learning methodology. The key idea is to decompose the solution into singular and regular parts. The neural network learning machinery incorporating the given jump conditions finds the singular solution, while the standard finite difference method is used to obtain the regular solution with associated boundary conditions. Regardless of the interface geometry, these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation, making the hybrid method easy to implement and efficient. The two- and three-dimensional numerical results show that the present hybrid method preserves second-order accuracy for the solution and its derivatives, and it is comparable with the traditional immersed interface method in the literature. As an application, we solve the Stokes equations with singular forces to demonstrate the robustness of the present method

A shallow physics-informed neural network for solving partial differential equations on surfaces

In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the surface normal and mean curvature used in the surface differential expressions can be computed easily. So instead of imposing the normal extension constraints used in literature, we write the surface differential operators in the form of traditional Cartesian differential operators and use them in the loss function directly. We perform a series of performance study for the present methodology by solving Laplace-Beltrami equation and surface diffusion equation on complex static surfaces. With just a moderate number of neurons used in the hidden layer, we are able to attain satisfactory prediction results. Then we extend the present methodology to solve the advection-diffusion equation on an evolving surface with given velocity. To track the surface, we additionally introduce a prescribed hidden layer to enforce the topological structure of the surface and use the network to learn the homeomorphism between the surface and the prescribed topology. The proposed network structure is designed to track the surface and solve the equation simultaneously. Again, the numerical results show comparable accuracy as the static cases. As an application, we simulate the surfactant transport on the droplet surface under shear flow and obtain some physically plausible results

Current Approaches to the Treatment of Head Injury in Children

Head trauma is one of the most challenging fields of traumatology and demands immediate attention and intervention by first-line clinicians. Symptoms can vary from victim to victim and according to the victim's age, leading to difficulties in making timely and accurate decisions at the point of care. In children, falls, accidents while playing, sports injuries, and abuse are the major causes of head trauma. Traffic accidents are the main cause of disability and death in adolescents and adults. Injury sites include facial bones, muscles, ligaments, vessels, joints, nerves, and focal or whole-brain injuries. Of particular importance are cranial and intracranial injuries. A closed injury occurs when the head suddenly and violently hits an object but the object does not break through the skull. A penetrating injury occurs when an object pierces the skull and affects the brain tissue. Early diagnosis and proper management are crucial to treat patients with potentially life-threatening head and neck trauma. In this review, we discuss the different cases of traumatic brain injury and summarize the current therapies and neuroprotective strategies as well as the related outcomes for children with traumatic brain injury

Prognostic values of a combination of intervals between respiratory illness and onset of neurological symptoms and elevated serum IgM titers in Mycoplasma pneumoniae encephalopathy

Background/PurposeTo retrospectively analyze the clinical manifestations of Mycoplasma pneumoniae (M. pneumoniae)-associated encephalopathy in pediatric patients.MethodsPediatric patients with positive serum anti-M. pneumoniae immunoglobulin M (IgM) were enrolled in this study. Clinical signs and symptoms, laboratory data, neuroimaging findings, and electrophysiological data were reviewed.ResultsOf 1000 patients identified, 11 (1.1%; male:female ratio = 7:4) had encephalopathy and were admitted to the pediatric intensive care unit. Clinical presentation included fever, symptoms of respiratory illness, and gastrointestinal upset. Neurological symptoms included altered consciousness, seizures, coma, focal neurological signs, and personality change. Neuroimaging and electroencephalographic findings were non-specific. Specimens of cerebrospinal fluid (CSF) for M. pneumoniae polymerase chain reaction (PCR) were negative. Higher M. pneumoniae IgM titers and longer intervals between respiratory and CNS manifestations were associated with worse outcomes.ConclusionClinical manifestations of M. pneumoniae-associated encephalopathy were variable. Diagnosis of M. pneumoniae encephalopathy should not rely on CSF detection of M. pneumoniae by PCR. M. pneumoniae IgM titers and intervals between respiratory and CNS manifestations might be possibly related to the prognosis of patients with M. pneumoniae-associated encephalopathy

A Shallow Ritz Method for Elliptic Problems with Singular Sources

In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features in the present work; namely, (i) the delta function singularity is naturally removed, (ii) level set function is introduced as a feature input, (iii) it is completely shallow, comprising only one hidden layer. We first introduce the energy functional of the problem and then transform the contribution of singular sources to a regular surface integral along the interface. In such a way, the delta function singularity can be naturally removed without introducing a discrete one that is commonly used in traditional regularization methods, such as the well-known immersed boundary method. The original problem is then reformulated as a minimization problem. We propose a shallow Ritz-type neural network with one hidden layer to approximate the global minimizer of the energy functional. As a result, the network is trained by minimizing the loss function that is a discrete version of the energy. In addition, we include the level set function of the interface as a feature input of the network and find that it significantly improves the training efficiency and accuracy. We perform a series of numerical tests to show the accuracy of the present method and its capability for problems in irregular domains and higher dimensions