Joint strategy fictitious play with inertia for potential games

We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion

Dynamics in atomic signaling games

We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with high probability or mutate with low probability. We analyze the long-run distribution of states and show that, for sufficiently small mutation probability, its support is limited to efficient communication systems. We find that this behavior is insensitive to the particular choice of evolutionary dynamic, a property that is due to the game having a potential structure with a potential function corresponding to average fitness. Consequently, the model supports conclusions similar to those found in the literature on language competition. That is, we show that efficient languages eventually predominate the society while reproducing the empirical phenomenon of linguistic drift. The emergence of efficiency in the atomic case can be contrasted with results for non-atomic signaling games that establish the non-negligible possibility of convergence, under replicator dynamics, to states of unbounded efficiency loss

Stimulus-invariant processing and spectrotemporal reverse correlation in primary auditory cortex

The spectrotemporal receptive field (STRF) provides a versatile and integrated, spectral and temporal, functional characterization of single cells in primary auditory cortex (AI). In this paper, we explore the origin of, and relationship between, different ways of measuring and analyzing an STRF. We demonstrate that STRFs measured using a spectrotemporally diverse array of broadband stimuli -- such as dynamic ripples, spectrotemporally white noise, and temporally orthogonal ripple combinations (TORCs) -- are very similar, confirming earlier findings that the STRF is a robust linear descriptor of the cell. We also present a new deterministic analysis framework that employs the Fourier series to describe the spectrotemporal modulations contained in the stimuli and responses. Additional insights into the STRF measurements, including the nature and interpretation of measurement errors, is presented using the Fourier transform, coupled to singular-value decomposition (SVD), and variability analyses including bootstrap. The results promote the utility of the STRF as a core functional descriptor of neurons in AI.Comment: 42 pages, 8 Figures; to appear in Journal of Computational Neuroscienc

Money and Goldstone modes

Why is ``worthless'' fiat money generally accepted as payment for goods and services? In equilibrium theory, the value of money is generally not determined: the number of equations is one less than the number of unknowns, so only relative prices are determined. In the language of mathematics, the equations are ``homogeneous of order one''. Using the language of physics, this represents a continuous ``Goldstone'' symmetry. However, the continuous symmetry is often broken by the dynamics of the system, thus fixing the value of the otherwise undetermined variable. In economics, the value of money is a strategic variable which each agent must determine at each transaction by estimating the effect of future interactions with other agents. This idea is illustrated by a simple network model of monopolistic vendors and buyers, with bounded rationality. We submit that dynamical, spontaneous symmetry breaking is the fundamental principle for fixing the value of money. Perhaps the continuous symmetry representing the lack of restoring force is also the fundamental reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure

Variation of Faba Beans (Vicia faba L.) Traits Induced By Heat, Electric Shock and Mutagen Nitrous Acid

This research was carried out to determine the impact of heat shock, electric shock and seeds in soaking nitrous acid mutagen solution on three cultivars of faba beans plant (Zaina, Aguadulce and Local) at the year 2012-2013. Factorial experiment was arranged in randomized complete block design (RCBD) with three replicates were used. The results showed that heat shock lead to early plants of 50% in flowering and an increase in the number of branches/plant and the number of seeds/pod compared to other treatments, whereas the seeds soaked in nitrous acid mutagen solution gave the highest plant height, leaf area index, number of pods/plant, seed weight, seed yield kg/ha, and did not differ significantly with treatment of electric shock in the protein yield(kg/ha). Zaina cultivar was superior over other cultivars in early to 50% flowering, number of branches/plant, number of pods/plant and seed weight, while gave the lowest value in plant height. Significant differences also observed for the interaction between cultivars and treatments. Zaina cultivar with heat shock treatment gave less number of days to 50% flowering, highest number of branches/plant and the number of seeds/pod, either when seeds soaked in nitrous acid mutagen solution given the highest plant height of plant, highest mean of seed weight, seed yield kg/ha and did not differ significantly with local variety in the number of pods/plant trait

Selection of Suitable Sites for Water Harvesting Structures in a Flood Prone Area Using Remote Sensing and GIS – Case Study

Water harvesting structures are extremely important to conserve precious natural resource like soil and water which is deteriorating due to the uncontrolled flood flushes that caused damages, in time where it could be very useful if suitable technical methods were applied to keep it. Check dams are one of these structures that could be very useful if certain conditions were available in the flood area. In this study Ali Al Gharbi which is located in the southeast part of Iraq near to the Iraqi- Iranian borders, is chosen as an area that suffered from frequently flood flushes that come from the Iranian land. Those floods damaged all the infrastructures like bridges, roads and also the farms and villages in its way. Remote sensing and GIS technologies were the appropriate tools to choose the suitable sites for check dams in the area. The various thematic maps such as Land use, Drainage, HSG, Slope and DEM maps were prepared for selecting suitable sites for construction of check dams. Four check dams and four percolation tanks were proposed for the construction that may serve the purpose of soil and water conservation to help in sustainable development of the catchment area. The proposed check dams can be very useful to supply water for irrigation in dry seasons. Keywords: Water harvesting, Check dams, Ali Al Gharbi, Missan Governorate, GIS, Floods, Remote sensing

The Case of the Missing Pitch Templates: How Harmonic Templates Emerge in the Early Auditory System

Periodicity pitch is the most salient and important of all pitch percepts.Psycho-acoustical models of this percept have long postulated the existenceof internalized harmonic templates against which incoming resolved spectracan be compared, and pitch determined according to the best matchingtemplates cite{goldstein:pitch}. However, it has been a mystery where andhow such harmonic templates can come about. Here we present a biologicallyplausible model for how such templates can form in the early stages of theauditory system. The model demonstrates that {it any} broadband stimulussuch as noise or random click trains, suffices for generating thetemplates, and that there is no need for any delay-lines, oscillators, orother neural temporal structures. The model consists of two key stages:cochlear filtering followed by coincidence detection. The cochlear stageprovides responses analogous to those seen on the auditory-nerve andcochlear nucleus. Specifically, it performs moderately sharp frequencyanalysis via a filter-bank with tonotopically ordered center frequencies(CFs); the rectified and phase-locked filter responses are further enhancedtemporally to resemble the synchronized responses of cells in the cochlearnucleus. The second stage is a matrix of coincidence detectors thatcompute the average pair-wise instantaneous correlation (or product)between responses from all CFs across the channels. Model simulations showthat for any broadband stimulus, high coincidences occur between cochlearchannels that are exactly harmonic distances apart. Accumulatingcoincidences over time results in the formation of harmonic templates forall fundamental frequencies in the phase-locking frequency range. Themodel explains the critical role played by three subtle but importantfactors in cochlear function: the nonlinear transformations following thefiltering stage; the rapid phase-shifts of the traveling wave near itsresonance; and the spectral resolution of the cochlear filters. Finally, wediscuss the physiological correlates and location of such a process and itsresulting templates

Auditory Short-Term Memory Behaves Like Visual Short-Term Memory

Are the information processing steps that support short-term sensory memory common to all the senses? Systematic, psychophysical comparison requires identical experimental paradigms and comparable stimuli, which can be challenging to obtain across modalities. Participants performed a recognition memory task with auditory and visual stimuli that were comparable in complexity and in their neural representations at early stages of cortical processing. The visual stimuli were static and moving Gaussian-windowed, oriented, sinusoidal gratings (Gabor patches); the auditory stimuli were broadband sounds whose frequency content varied sinusoidally over time (moving ripples). Parallel effects on recognition memory were seen for number of items to be remembered, retention interval, and serial position. Further, regardless of modality, predicting an item's recognizability requires taking account of (1) the probe's similarity to the remembered list items (summed similarity), and (2) the similarity between the items in memory (inter-item homogeneity). A model incorporating both these factors gives a good fit to recognition memory data for auditory as well as visual stimuli. In addition, we present the first demonstration of the orthogonality of summed similarity and inter-item homogeneity effects. These data imply that auditory and visual representations undergo very similar transformations while they are encoded and retrieved from memory