Transactional Interpretation for the Principle of Minimum Fisher Information.

The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can be applied to transaction processes, the dynamics of which can be interpreted as the market tendency to minimize the information revealed about itself. More information involves higher costs (information is physical). The starting point for our considerations is a description of the market derived from the assumption of minimum Fisher information for a strategy with a fixed financial risk. Strategies of this type that minimize Fisher information overlap with the well-known eigenstates of a the quantum harmonic oscillator. The analytical extension of this field of strategy to the complex vector space (traditional for quantum mechanics) suggests the study of the interference of the oscillator eigenstates in terms of their minimization of Fisher information. It is revealed that the minimum value of Fisher information of the superposition of the two strategies being the ground state and the second excited state of the oscillator, has Fisher information less than the ground state of the oscillator. Similarly, less information is obtained for the system of strategies (the oscillator eigenstates) randomized by the Gibbs distribution. We distinguish two different views on the description of Fisher information. One of them, the classical, is based on the value of Fisher information. The second, we call it transactional, expresses Fisher information from the perspective of the constant risk of market strategies. The orders of the market strategies derived from these two descriptions are different. From a market standpoint, minimizing Fisher information is equivalent to minimizing risk.

Non-Classical Rules in Quantum Games.

Over the last twenty years, quantum game theory has given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing bimatrix games introduced by J. Eisert, M. Wilkens and M. Lewenstein. The scheme assumes that players' strategies are unitary operations and the players act on the maximally entangled two-qubit state. The quantum nature of the scheme has been under discussion since the article by Eisert et al. came out. The aim of our paper was to identify some of non-classical features of the quantum scheme.

Quantum Games with Unawareness.

Games with unawareness model strategic situations in which players' perceptions about the game are limited. They take into account the fact that the players may be unaware of some of the strategies available to them or their opponents as well as the players may have a restricted view about the number of players participating in the game. The aim of the paper is to introduce this notion into theory of quantum games. We focus on games in strategic form and Eisert-Wilkens-Lewenstein type quantum games. It is shown that limiting a player's perception in the game enriches the structure of the quantum game substantially and allows the players to obtain results that are unattainable when the game is played in a quantum way by means of previously used methods.

Comment on "constructing quantum games from nonfactorizable joint probabilities".

In the paper [Phys. Rev. E 76, 061122 (2007)], the authors presented a way of playing 2 × 2 games so that players were able to exploit nonfactorizable joint probabilities respecting the nonsignaling principle (i.e., relativistic causality). We are going to prove, however, that the scheme does not generalize the games studied in the commented paper. Moreover, it allows the players to obtain nonclassical results even if the factorizable joint probabilities are used.

Morphometric analysis of the gonadal veins in human foetuses.

Professional literature data demonstrates morphometric features of the gonadal veins in adults. The length of the gonadal veins and their outlet angles in 130 human foetuses (71 males, 59 females), between the 4th and 6th month of prenatal life, were studied by means of anatomical, digital and statistical methods. In all specimens the left gonadal veins entered the left renal artery, and the right gonadal veins terminated in the inferior vena cava. In all age ranges the left gonadal veins were longer than the right ones (P < or = 0.01), and the outlet angles of the left gonadal veins were larger than these angles on the right side (P < or = 0.01). The correlation coefficient between the length of the left and right testicular veins was r1 = 0.975 (P < or = 0.01). The correlation coefficients between the length of the testicular veins and foetal age were r2 = 0.591 for the right testicular vein and r3 = 0.578 for the left testicular vein (P < or = 0.01). A low correlation between the outlet angles of the testicular veins and foetal age was observed, for the right side r4 = 0.187, and for the left side r5 = 0.177 (P < or = 0.05). The correlation coefficient between the length of the left and right ovarian veins in foetuses aged 4-6 months was r6 = 0.855 (P < or = 0.01). The correlation coefficients between the length of the ovarian veins and foetal age were r7 = 0.578 for the right ovarian vein and r8 = 0.566 for the left ovarian vein (P < or = 0.01). No correlation between the outlet angles of the ovarian veins and foetal age was observed (P > 0.05).

The retroperitoneal anastomoses of the gonadal veins in human foetuses.

In the retroperitoneal space the gonadal veins form a collateral circulation that has a great clinical impact on sclerotherapy or surgical ligation of varicoceles. The aim of this study was to examine the communications of the gonadal veins (according to classification, frequency of appearance, gender and syntopic differences) in human foetuses of both sexes (71 males and 59 females) aged 4--6 months of intrauterine life. On the right side the most frequently were found the gonadal-periureteral anastomosis (23%) and the gonadal-perirenal anastomosis (22%). A gonadal-lumbar anastomosis on the right side appeared in 7% of cases. On the left side the most frequent (37%) was the gonadalperirenal anastomosis, more frequently occurring as an ovarian-perirenal anastomosis (48%) than as a testicular-perirenal anastomosis (29%). Gonadal-periureteral anastomoses were found in a quarter of cases. Gonadal-lumbar anastomoses were observed in 7% of individuals. On the left side the gonadal-mesenteric inferior anastomosis was specifically observed (21%) as an ovarian-mesenteric inferior anastomosis (24%) and a testicular-mesenteric inferior anastomosis (19%). The cross-communications between the right and left gonadal veins (7%) were more frequently as the bilateral testicular (9.7%) than as the bilateral ovarian one (3%). In female foetuses gonadal-perirenal anastomoses occurred with statistically greater frequency than gonadal-periureteral anastomoses (p<=0.05). The frequency of cross-communications of the gonadal veins was three times greater in male foetuses (p

Skeletopic analysis of the gonadal veins in human foetuses.

During ontogenesis an imbalance is observable in the development of the skeletal and vascular systems. By means of anatomical and radiological methods the gonadal veins were studied in relation to the vertebral column in 60 human foetuses of both sexes aged from 4 to 6 months of prenatal life. In male foetuses aged 4--5 months the origin of the gonadal veins projected onto the sacral apex (r(1)=0.95, r(3)=0.85), and in 6(th) month they extended below the vertebral column (r(1')=0.80, r(3')=0.90). In female foetuses the origin of the gonadal veins in the 4(th) month projected symmetrically onto S(1) (r(5)=0.70, r(7)=0.70). In the 5(th) month of intrauterine life the origin of the left ovarian vein was found at S2 (r(7')=0.80) and the origin of the right one at S1-S2 (r(5')=0.80). In the 6th month the origin of the left ovarian vein was located at S(3) (r(7')=0.80) and the right one at S(2)-S(3) (r(5'')=0.90). The skeletopic analysis of the origin of the gonadal veins demonstrated gender (the origin was higher in females) and syntopic (the origin was higher on the right side) differences (p0.05). On the right side the termination of the gonadal (testicular and ovarian) veins projected constantly onto L(2). On the left side the termination of the left gonadal (testicular and ovarian) veins apparently descended by one vertebra (pseudodescensus).