Quantum Bound States with Zero Binding Energy

After reviewing the general properties of zero-energy quantum states, we give the explicit solutions of the \seq with $E=0$ for the class of potentials $V=-|\gamma|/r^{\nu}$, where $-\infty 2$, these solutions are normalizable and correspond to bound states, if the angular momentum quantum number $l>0$. [These states are normalizable, even for $l=0$, if we increase the space dimension, $D$, beyond 4; i.e. for $D>4$.] For $\nu <-2$ the above solutions, although unbound, are normalizable. This is true even though the corresponding potentials are repulsive for all $r$. We discuss the physics of these unusual effects.Comment: 11 pages, 4 figures which can be generated from Mathematica commands given at the end of the file. Latex, REVISED--Fig. 4 Mathematica command improved and correcte

Command Interneurons in the Crayfish Central Nervous System

The motor effects evoked by stimulation of each of eight command fibres in the circumoesophageal commissures of the crayfish are described. The fibres obtained appeared to have widespread connexions in all or most of the lower ganglia. For certain fibres the response was stronger on the homolateral side of the animal; for others it was symmetrical. The frequency of stimulation of a command fibre generally had a pronounced influence on the speed of the evoked response. In addition, segments of the total response could be elicited selectively by alteration of the frequency and duration of stimulation. Although the responses associated with most of the fibres were not sensitive to the fine temporal pattern of the applied stimulation, for one fibre the motor output depended clearly on the spacing of the stimulating pulses

Postsynaptic Ca2+, but not cumulative depolarization, is necessary for the induction of associative plasticity in Hermissenda

The neuronal modifications that underlie associative memory in Hermissenda have their origins in a synaptic interaction between the visual and vestibular systems, and can be mimicked by contiguous in vitro stimulation of these converging pathways. At the offset of vestibular stimulation (i.e., hair cell activity), the B photoreceptors are briefly released from synaptic inhibition resulting in a slight depolarization (2–4 mV). If contiguous pairings of light-induced depolarization and presynaptic vestibular activity occur in close temporal succession, this depolarization “accumulates” and has been hypothesized to culminate in a sustained rise in intracellular Ca2+ and a resultant Ca(2+)-mediated phosphorylation of K+ channels as well as an associated increase in input resistance. Here we demonstrate that this cumulative depolarization is neither necessary nor sufficient for the biophysical modifications of the B cell membrane indicative of memory formation. Consistent with several recent reports of one-trial learning in Hermissenda, one pairing of light with mechanical stimulation of the vestibular hair cells resulted in a rise in neuronal input resistance across the B cell membrane that was attenuated by a prepairing iontophoretic injection of the Ca2+ chelator EGTA (25 mM), indicating that this potentiation was Ca2+ dependent. However, the use of a single pairing negates the possibility of an accumulation of depolarization across trials. In a subsequent experiment, B photoreceptors underwent a cumulative depolarization, and a coincident rise in input resistance, during multiple pairings of light and hair cell stimulation. However, if the B photoreceptor was voltage clamped at its initial resting potential before and after each pairing, thus eliminating the cumulative depolarization, the rise in resistance not only persisted, but was enhanced. Moreover, if unpaired light presentations were followed by a current-induced depolarization (to mimic cumulative depolarization), no increase in input resistance was detected. To assess directly the effect of a cumulative depolarization on the voltage-dependent Ca2+ current, an analysis of the inward current on the B cell soma membrane was conducted. It was determined that (1) the inward current may undergo a partial inactivation during sustained depolarization, (2) the peak current was depressed during repetitive depolarizations, and (3) the peak current underwent a steady- state inactivation, such that it was reduced when elicited from holding potentials more positive than -60 mV. The analysis of this current suggests that pairings of light and presynaptic activity would reduce voltage-dependent Ca2+ influx when those pairings are conducted at depolarized membrane potentials, such as during cumulative depolarization

A low-voltage activated, transient calcium current is responsible for the time-dependent depolarizing inward rectification of rat neocortical neurons in vitro

Intracellular recordings were obtained from rat neocortical neurons in vitro. The current-voltage-relationship of the neuronal membrane was investigated using current- and single-electrode-voltage-clamp techniques. Within the potential range up to 25 mV positive to the resting membrane potential (RMP: –75 to –80 mV) the steady state slope resistance increased with depolarization (i.e. steady state inward rectification in depolarizing direction). Replacement of extracellular NaCl with an equimolar amount of choline chloride resulted in the conversion of the steady state inward rectification to an outward rectification, suggesting the presence of a voltage-dependent, persistent sodium current which generated the steady state inward rectification of these neurons. Intracellularly injected outward current pulses with just subthreshold intensities elicited a transient depolarizing potential which invariably triggered the first action potential upon an increase in current strength. Single-electrode-voltage-clamp measurements reveled that this depolarizing potential was produced by a transient calcium current activated at membrane potentials 15–20 mV positive to the RMP and that this current was responsible for the time-dependent increase in the magnitude of the inward rectification in depolarizing direction in rat neocortical neurons. It may be that, together with the persistent sodium current, this calcium current regulates the excitability of these neurons via the adjustment of the action potential threshold

ImageSpirit: Verbal Guided Image Parsing

Humans describe images in terms of nouns and adjectives while algorithms operate on images represented as sets of pixels. Bridging this gap between how humans would like to access images versus their typical representation is the goal of image parsing, which involves assigning object and attribute labels to pixel. In this paper we propose treating nouns as object labels and adjectives as visual attribute labels. This allows us to formulate the image parsing problem as one of jointly estimating per-pixel object and attribute labels from a set of training images. We propose an efficient (interactive time) solution. Using the extracted labels as handles, our system empowers a user to verbally refine the results. This enables hands-free parsing of an image into pixel-wise object/attribute labels that correspond to human semantics. Verbally selecting objects of interests enables a novel and natural interaction modality that can possibly be used to interact with new generation devices (e.g. smart phones, Google Glass, living room devices). We demonstrate our system on a large number of real-world images with varying complexity. To help understand the tradeoffs compared to traditional mouse based interactions, results are reported for both a large scale quantitative evaluation and a user study.Comment: http://mmcheng.net/imagespirit

Financial Integration and Financial Crisis: Croatia Approaching The EMU

The breakdown of command economies has significantly increased growth potentials all over Europe and opened up prospects for economic development. Encouraged by that, the EU embarked on the process of deeper economic integration. Its main aspects – economic liberalization and monetary integration – coincided with the worldwide globalization of trade and capital flows. As a laggard country in the process of economic integration, Croatia is in a particularly difficult position – besides soaring trade deficit, it is highly indebted and strongly dependant upon foreign capital. Appreciating theoretical inferences and empirical evidence on monetary integration, while taking reference to the realized level of international financial integration and external vulnerability, the aim of the paper is to find out if Croatia fulfils the criteria for successful monetary integration.optimum currency area, financial integration, external balance, EMU, Central and Eastern Europe

Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary

Vapor bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. The method uses finite time steps and features an iterative technique for applying the boundary conditions at infinity directly to the liquid at a finite distance from the free surface. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)^1/2 where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For Δp/ρ = 10^6 (cm/sec)^2 ~ 1 atm./density of water the jet had a speed of about 130 m/sec in the first case and 170 m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapor are not important