Cubic Hermite Finite Element Method for Nonlinear Black-Scholes Equation Governing European Options

A numerical algorithm for solving a generalized Black-Scholes partial differential equation, which arises in European option pricing considering transaction costs is developed. The Crank-Nicolson method is used to discretize in the temporal direction and the Hermite cubic interpolation method to discretize in the spatial direction. The efficiency and accuracy of the proposed method are tested numerically, and the results confirm the theoretical behaviour of the solutions, which is also found to be in good agreement with the exact solution.

Will I Feel This in my Dreams? Examining Temporal Associations between Daytime and Dream Affect

Despite the theory that dreams function to process emotions, few studies have examined how emotional experiences during daytime (“daytime affect”) are associated with the emotional tone of dreams (“dream affect”) that night, and vice versa. This study examined bidirectional associations between dream affect and daytime positive and negative affect. Participants were 84 nurses who completed two weeks of ecological momentary assessments. If participants remembered the previous night’s dreams (nparticipants=68; ndays=391), they reported the dream’s emotional tone upon waking (‘0’=very negative to ‘100’=very positive). Participants also responded to the Positive and Negative Affect Scale three times/day. Multilevel modeling simultaneously tested two temporal directions (daytime affect→dream affect, dream affect→daytime affect) at the within- and between-person levels. After adjusting for socio-demographic and work characteristics, at the within-person level, dream affect was more positive than usual on nights following more positive daytime affect (B=0.25, p=.003). In the other temporal direction, dream affect was not associated with the following day’s positive affect. At the between-person level, nurses who reported more positive dream affect also reported more positive daytime affect (B=0.24, p=.025). No associations emerged with negative affect. Findings suggest that daytime affect is associated with the emotional tone of that night’s dreams, but only in the context of positive affect. Importantly, negative affect was relatively low in this sample, so different patterns may emerge for people more prone to negative affect. Overall, these novel findings support the theory that dreams serve to process emotions, providing insight into the mystery of the function of dreams.

Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations

Objective The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions. Results The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology of Mickens procedure is used in the spatial direction and also within the first order temporal direction that construct the first-order finite difference approximation to solve the considered problem numerically. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. Numerical experiments were conducted to support the theoretical results.

Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay

The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using the L2−1σ approximation of the time Caputo derivative, a finite difference method with second-order accuracy in the temporal direction is achieved. The novelty of this paper is to introduce a numerical scheme for the problem under consideration with variable coefficients, nonlinear source term, and delay time constant. The numerical results show that the global convergence orders for spatial and time dimensions are approximately fourth order in space and second-order in time.

Quantum superposition of thermodynamic evolutions with opposing time’s arrows

Microscopic physical laws are time-symmetric, hence, a priori there exists no preferential temporal direction. However, the second law of thermodynamics allows one to associate the “forward” temporal direction to a positive variation of the total entropy produced in a thermodynamic process, and a negative variation with its “time-reversal” counterpart. This definition of a temporal axis is normally considered to apply in both classical and quantum contexts. Yet, quantum physics admits also superpositions between forward and time-reversal processes, whereby the thermodynamic arrow of time becomes quantum-mechanically undefined. In this work, we demonstrate that a definite thermodynamic time’s arrow can be restored by a quantum measurement of entropy production, which effectively projects such superpositions onto the forward (time-reversal) time-direction when large positive (negative) values are measured. Finally, for small values (of the order of plus or minus one), the amplitudes of forward and time-reversal processes can interfere, giving rise to entropy-production distributions featuring a more or less reversible process than either of the two components individually, or any classical mixture thereof.

Optocollic responses in adult barn owls (Tyto furcata)

Barn owls, like primates, have frontally oriented eyes, which allow for a large binocular overlap. While owls have similar binocular vision and visual-search strategies as primates, it is less clear whether reflexive visual behavior also resembles that of primates or is more similar to that of closer related, but lateral-eyed bird species. Test cases are visual responses driven by wide-field movement: the optokinetic, optocollic, and optomotor responses, mediated by eye, head and body movements, respectively. Adult primates have a so-called symmetric horizontal response: they show the same following behavior, if the stimulus, presented to one eye only, moves in the nasal-to-temporal direction or in the temporal-to-nasal direction. By contrast, lateral-eyed birds have an asymmetric response, responding better to temporal-to-nasal movement than to nasal-to-temporal movement. We show here that the horizontal optocollic response of adult barn owls is less asymmetric than that in the chicken for all velocities tested. Moreover, the response is symmetric for low velocities (< 20 deg/s), and similar to that of primates. The response becomes moderately asymmetric for middle-range velocities (20–40 deg/s). A definitive statement for the complex situation for higher velocities (> 40 deg/s) is not possible.

Corporate hypocrisy

This review article aimed to contribute to the understanding of the importance of coherence between saying and acting to prevent companies from being perceived from the perspective of business hypocrisy and affecting the brand, reputation, trust and credibility in the company. It was carried out based on the Methodi Ordinatio, addressing its theoretical origins and then approaching the concept, later venturing into the different studies that have approached it from corporate social responsibility (CSR), ethics; reputation, interest groups (stakeholders), and communication, subsequently in relation to the consequences that it generates in world-known organizations, their statements and the criticism made, subsequently an analysis of three aspects or facets is made in which it is presented namely: moral hypocrisy; behavioral hypocrisy and how to attribute business hypocrisy, the next point presents a typology that involves two dimensions: an orientation that refers to the attention span, in the short and long term of participants when making or responding to accusations of hypocrisy and a temporal direction, which refers to the point of comparison, past or future, finally reaches some conclusions, and some practical implications.

Temporal irreversibility of neural dynamics as a signature of consciousness

Even though the fundamental laws of physics are the same when the direction of time is inverted, dissipative systems evolve in the preferred temporal direction indicated by the thermodynamic arrow of time. The fundamental nature of this temporal asymmetry led us to hypothesize its presence in the neural activity evoked by conscious perception of the physical world, and thus its covariance with the level of conscious awareness. Inspired by recent developments in stochastic thermodynamics, we implemented a data-driven and model-free deep learning framework to decode the temporal inversion of electrocorticography signals acquired from non-human primates. Brain activity time series recorded during conscious wakefulness could be distinguished from their inverted counterparts with high accuracy, both using frequency and phase information. However, classification accuracy was reduced for data acquired during deep sleep and under ketamine-induced anesthesia; moreover, the predictions obtained from multiple independent neural networks were less consistent for sleep and anesthesia than for conscious wakefulness. Finally, the analysis of feature importance scores highlighted transitions between slow (≈20 Hz) and fast frequencies (> 40 Hz) as the main contributors to the temporal asymmetry observed during conscious wakefulness. Our results show that a preferred temporal direction is simultaneously manifest in the neural activity evoked by conscious mentation and in the phenomenology of the passage of time, establishing common ground to tackle the relationship between brain and subjective experience.

DatalogMTL with Negation Under Stable Models Semantics

We introduce negation under stable models semantics in DatalogMTL—a temporal extension of Datalog with metric operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rationals and decidable in EXPSPACE in data complexity over the integers. We also show that, if we restrict our attention to forward-propagating programs (where rules propagate information in a single temporal direction), reasoning over integers becomes PSPACE-complete in data complexity and hence no harder than over positive programs; however, reasoning over the rationals in this fragment remains undecidable.