The Coherence Field in the Field Perturbation Theory of Superconductivity

We re-examine the Nambu-Gorkov perturbation theory of superconductivity on the basis of the Bogoliubov-Valatin quasi-particles. We show that two different fields (and two additional analogous fields) may be constructed, and that the Nambu field is only one of them. For the other field- the coherence field- the interaction is given by means of two interaction vertices that are based on the Pauli matrices tau1 and tau3. Consequently, the Hartree integral for the off-diagonal pairing self-energy may be finite, and in some cases large. We interpret the results in terms of conventional superconductivity, and also discuss briefly possible implications to HTSC

Multistable attractors in a network of phase oscillators with three-body interaction

Three-body interactions have been found in physics, biology, and sociology. To investigate their effect on dynamical systems, as a first step, we study numerically and theoretically a system of phase oscillators with three-body interaction. As a result, an infinite number of multistable synchronized states appear above a critical coupling strength, while a stable incoherent state always exists for any coupling strength. Owing to the infinite multistability, the degree of synchrony in asymptotic state can vary continuously within some range depending on the initial phase pattern.Comment: 5 pages, 3 figure

The Field Perturbation Theory of the Double Correlated Phase in High Temperature Superconductors

The Double-Correlated phase in HTSC, and its treatment by field perturbation theory, is established. In particular, we define the ground state, the quasi-particle excitations, and construct an appropriate field. We also derive the unperturbed Hamiltonian, and the propagators for the unperturbed state. Then we discuss the perturbation Hamiltonian, and show that the Hartree diagram is significant for both the pseudogap and the superconductive order parameter, and suggest that it yields the major contribution to these parameters.Comment: 23 pages Of MSWord in PDF format, 1 figur

Morphometric and macroanatomic examination of auditory ossicles in male wolves (Canis lupus)

Background: The aim of the study was to determine morphometric and macroanatomic features of auditory ossicles and the tympanic bulla in wolf. Materials and methods: For this purpose, 7 skulls of adult male wolf were used in the study. Auditory ossicles was photographed on a dissection microscope after it was removed from the skull. A total of 14 morphometric measurements were taken among the different points of malleus, incus and stapes in Image J programme. Mean values of the measurements were obtained and statistically compared in terms of sides (right-left). Results: In male wolves, the lengths of the right and left malleus were determined as mean 9.35 ± 0.14 and 9.57 ± 0.25 mm, the lengths of the incus as mean 3.01 ± 0.32 and 2.94 ± 0.16 mm, and the lengths of the stapes as mean 2.57 ± 0.12 and 2.59 ± 0.14 mm, respectively. The differences were not statistically significant when all the morphometric parameters were compared in terms of sides (p > 0.05). Conclusions: It is considered that this study will contribute to the anatomical studies to be conducted in the Canidae family regarding auditory ossicles

Dynamical Synapses Enhance Neural Information Processing: Gracefulness, Accuracy and Mobility

Experimental data have revealed that neuronal connection efficacy exhibits two forms of short-term plasticity, namely, short-term depression (STD) and short-term facilitation (STF). They have time constants residing between fast neural signaling and rapid learning, and may serve as substrates for neural systems manipulating temporal information on relevant time scales. The present study investigates the impact of STD and STF on the dynamics of continuous attractor neural networks (CANNs) and their potential roles in neural information processing. We find that STD endows the network with slow-decaying plateau behaviors-the network that is initially being stimulated to an active state decays to a silent state very slowly on the time scale of STD rather than on the time scale of neural signaling. This provides a mechanism for neural systems to hold sensory memory easily and shut off persistent activities gracefully. With STF, we find that the network can hold a memory trace of external inputs in the facilitated neuronal interactions, which provides a way to stabilize the network response to noisy inputs, leading to improved accuracy in population decoding. Furthermore, we find that STD increases the mobility of the network states. The increased mobility enhances the tracking performance of the network in response to time-varying stimuli, leading to anticipative neural responses. In general, we find that STD and STP tend to have opposite effects on network dynamics and complementary computational advantages, suggesting that the brain may employ a strategy of weighting them differentially depending on the computational purpose.Comment: 40 pages, 17 figure

Dynamics of Neural Networks with Continuous Attractors

We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.Comment: 6 pages, 7 figures with 4 caption

A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks

Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.Comment: 43 pages, 10 figure

How do people learn how to plan?

How does the brain learn how to plan? We reverse-engineer people's underlying learning mechanisms by combining rational process models of cognitive plasticity with recently developed empirical methods that allow us to trace the temporal evolution of people's planning strategies. We find that our Learned Value of Computation model (LVOC) accurately captures people's average learning curve. However, there were also substantial individual differences in metacognitive learning that are best understood in terms of multiple different learning mechanisms -- including strategy selection learning. Furthermore, we observed that LVOC could not fully capture people's ability to adaptively decide when to stop planning. We successfully extended the LVOC model to address these discrepancies. Our models broadly capture people's ability to improve their decision mechanisms and represent a significant step towards reverse-engineering how the brain learns increasingly more effective cognitive strategies through its interaction with the environment

Contact Nonlinearities of Rough Conductors in Antennas and Connectors

Contacts of conductors with rough surfaces cause losses and nonlinear distortion of the high-power signals at high frequencies. The contact nonlinearities are analysed in a pair and array of the contact asperities in metal-insulator-metal (MIM) junctions. An improved model of the tunnelling resistivity is proposed and its accuracy is demonstrated for the harmonic signals. The model is also applied to the analysis of the thermal effect on the contact resistivity of rough conductors

Evidence for surprise minimization over value maximization in choice behavior

Classical economic models are predicated on the idea that the ultimate aim of choice is to maximize utility or reward. In contrast, an alternative perspective highlights the fact that adaptive behavior requires agents' to model their environment and minimize surprise about the states they frequent. We propose that choice behavior can be more accurately accounted for by surprise minimization compared to reward or utility maximization alone. Minimizing surprise makes a prediction at variance with expected utility models; namely, that in addition to attaining valuable states, agents attempt to maximize the entropy over outcomes and thus 'keep their options open'. We tested this prediction using a simple binary choice paradigm and show that human decision-making is better explained by surprise minimization compared to utility maximization. Furthermore, we replicated this entropy-seeking behavior in a control task with no explicit utilities. These findings highlight a limitation of purely economic motivations in explaining choice behavior and instead emphasize the importance of belief-based motivations