On Completely Mixed Stochastic Games

In this paper, we consider a zero-sum undiscounted stochastic game which has finite state space and finitely many pure actions. Also, we assume the transition probability of the undiscounted stochastic game is controlled by one player and all the optimal strategies of the game are strictly positive. Under all the above assumptions, we show that the $\beta$-discounted stochastic games with the same payoff matrices and $\beta$ sufficiently close to 1 are also completely mixed. We give a counterexample to show that the converse of the above result in not true. We also show that, if we have non-zero value in some state for the undiscounted stochastic game then for $\beta$ sufficiently close to 1 the $\beta$-discounted stochastic game also possess nonzero value in the same state

On threshold resummation beyond leading 1-x order

We check against exact finite order three-loop results for the non-singlet F_2 and F_3 structure functions the validity of a class of momentum space ansaetze for threshold resummation at the next-to-leading order in 1-x, which generalize results previously obtained in the large-\beta_0 limit. We find that the ansaetze do not work exactly, pointing towards an obstruction to threshold resummation at this order, but still yield correct results at the leading logarithmic level for each color structures, as well as at the next-to-next-to-leading logarithmic level for the specific C_F^3 color factor. A universality of the leading logarithm contributions to the physical evolution kernels of F_2 and F_3 at the next-to-leading order in 1-x is observed.Comment: v1:18 pages; v2: 26 pages, expanded version with new results for the F_3 structure function and added references; v3: more concise sections 3 and 4, improved discussion in section 5, added references, to be published in JHE

Automatic Discrimination of Abnormal Subjects Using the Visual Evoked Potential Spectral Components

Study of visual evoked potential (VEP) is one of the utilized methods in clinical diagnosis of ophthalmology and neurological disorders. The automatic detection of VEP spectral components is an important tool in the diagnosis of mental activity. This paper presents a novel computational approach using feedforward neural network to identify abnormal subjects from changes in spectral components. The output vector from the feedforward neural network is based on the VEP spectral components. The software was developed to identify mental state from the VEP spectral components using Matlab software package. Using this approach, it is possible to perform real-time abnormality identification accurately on personal computers

Orderfield property of mixtures of stochastic games

We consider certain mixtures, Γ, of classes of stochastic games and provide sufficient conditions for these mixtures to possess the orderfield property. For 2-player zero-sum and non-zero sum stochastic games, we prove that if we mix a set of states S1 where the transitions are controlled by one player with a set of states S2 constituting a sub-game having the orderfield property (where S1∩S2=∅), the resulting mixture Γ with states S=S1∪S2 has the orderfield property if there are no transitions from S2 to S1. This is true for discounted as well as undiscounted games. This condition on the transitions is sufficient when S1 is perfect information or SC (Switching Control) or ARAT (Additive Reward Additive Transition). In the zero-sum case, S1 can be a mixture of SC and ARAT as well. On the other hand,when S1 is SER-SIT (Separable Reward - State Independent Transition), we provide a counter example to show that this condition is not sufficient for the mixture Γ to possess the orderfield property. In addition to the condition that there are no transitions from S2 to S1, if the sum of all transition probabilities from S1 to S2 is independent of the actions of the players, then Γ has the orderfield property even when S1 is SER-SIT. When S1 and S2 are both SERSIT, their mixture Γ has the orderfield property even if we allow transitions from S2 to S1. We also extend these results to some multi-player games namely, mixtures with one player control Polystochastic games. In all the above cases, we can inductively mix many such games and continue to retain the orderfield property

Spatial and temporal variations of small-scale plasma turbulence parameters in the equatorial electrojet: HF and VHF radar observational results

The spatial and temporal variations of various parameters associated with plasma wave turbulence in the equatorial electrojet (EEJ) at the magnetic equatorial location of Trivandrum (8.5° N, 77° E; dip 0.5° N) are studied for the first time, using co-located HF (18MHz) and VHF (54.95MHz) coherent backscatter radar observations (daytime) in the altitude region of 95-110km, mostly on magnetically quiet days. The derived turbulence parameters are the mean electron density irregularity strength (δn/n), anomalous electron collision frequency (ν<sub><i>e</i></sub>*) and the corrected east-west electron drift velocity (<i>V<sub>ey</sub></i>). The validity of the derived parameters is confirmed using radar data at two different frequencies and comparing with in-situ measurements. The behaviour of δn/n in relation to the backscattered power during weak and strong EEJ conditions is also examined to understand the growth and evolution of turbulence in the electrojet

Threshold corrections to rapidity distributions of Z and W^\pm bosons beyond N^2 LO at hadron colliders

Threshold enhanced perturbative QCD corrections to rapidity distributions of $Z$ and $W^\pm$ bosons at hadron colliders are presented using the Sudakov resummed cross sections at N${}^3$LO level. We have used renormalisation group invariance and the mass factorisation theorem that these hard scattering cross sections satisfy to construct the QCD amplitudes. We show that these higher order threshold QCD corrections stabilise the theoretical predictions for vector boson production at the LHC under variations of both renormalisation and factorisation scales.Comment: 17 pages, 8 eps figures. This paper is dedicated to the memory of W.L.G.A.M. van Neerve