When Can Limited Randomness Be Used in Repeated Games?

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at generating random-like sequences, and true random bits may be unavailable. Even if the players have access to enough random bits for a single instance of the game their randomness might be insufficient if the game is played many times. In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games. We show that for a large class of games containing arbitrary two-player zero-sum games, approximate Nash equilibria of the $n$-stage repeated version of the game exist if and only if both players have $\Omega(n)$ random bits. In contrast, we show that there exists a class of games for which no equilibrium exists in pure strategies, yet the $n$-stage repeated version of the game has an exact Nash equilibrium in which each player uses only a constant number of random bits. When the players are assumed to be computationally bounded, if cryptographic pseudorandom generators (or, equivalently, one-way functions) exist, then the players can base their strategies on "random-like" sequences derived from only a small number of truly random bits. We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then $\Omega(n)$ random bits remain necessary for equilibria to exist

Bicalutamide as an Androgen Blocker With Secondary Effect of Promoting Feminization in Male-to-Female Transgender Adolescents

PURPOSE: The purpose of the study was to describe the novel use of bicalutamide in transgender youth. METHODS: This is a retrospective review of patients with gender dysphoria followed in the pediatric endocrine clinic at Riley Hospital for Children. RESULTS: Of 104 patients with gender dysphoria, 23 male-to-female adolescents received bicalutamide 50 mg daily as a second-line puberty blocker after insurance company denial of a gonadotropin-releasing hormone analog. Six patients received estrogen concurrently. Of 13 patients treated exclusively with bicalutamide seen in follow-up, 84.6% had breast development within 6 months, the majority being ≥ Tanner stage III. CONCLUSIONS: Bicalutamide may be an alternative to gonadotropin-releasing hormone analogs in transgender male-to-female youth who are also ready to undergo physical transition

Data-driven efficient score tests for deconvolution problems

We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution with the known noise density and efficient score tests for the case of unknown density. The tests are incorporated with model selection rules to choose reasonable model dimensions automatically by the data. Consistency of the tests is proved

Wood Quality in Pine Stands Damaged by Industrial Pollutants in Poland

Information on the impact of industrial air pollutants on forest stands aid consequences on wood quality are a little mixed up and misleading. Some experiments made on pines 130-230 years old did not reveal serious changes of wood quality. In this work, we present results of investigations on wood from 60-year-old pine trees which were under the influence of air pollutants for about 40 years. Such pine stands, of an age near the mean for the present forests in Poland, were the basis for some evaluations of financial losses in Poland due to the effects of air pollution on forests. Detailed data on the properties of the pine wood, which were the basis of the above-mentioned calculations, are also presented. The factors influencing economic losses are given based on the findings presented

Neuroinflammation and white matter alterations in obesity assessed by Diffusion Basis Spectrum Imaging

Human obesity is associated with low-grade chronic systemic inflammation, alterations in brain structure and function, and cognitive impairment. Rodent models of obesity show that high-calorie diets cause brain inflammation (neuroinflammation) in multiple regions, including the hippocampus, and impairments in hippocampal-dependent memory tasks. To determine if similar effects exist in humans with obesity, we applied Diffusion Basis Spectrum Imaging (DBSI) to evaluate neuroinflammation and axonal integrity. We examined diffusion-weighted magnetic resonance imaging (MRI) data in two independent cohorts of obese and non-obese individuals (Cohort 1: 25 obese/21 non-obese; Cohort 2: 18 obese/41 non-obese). We applied Tract-based Spatial Statistics (TBSS) to allow whole-brain white matter (WM) analyses and compare DBSI-derived isotropic and anisotropic diffusion measures between the obese and non-obese groups. In both cohorts, the obese group had significantly greater DBSI-derived restricted fraction (DBSI-RF; an indicator of neuroinflammation-related cellularity), and significantly lower DBSI-derived fiber fraction (DBSI-FF; an indicator of apparent axonal density) in several WM tracts (all correcte

Penicillin-binding proteins of protoplast and sporoplast membranes of Streptomyces griseus strains

Membrane-bound penicillin-binding proteins (PBPs) of two Streptomyces griseus strains that sporulate well in liquid and solid medium have been investigated during the course of their life-cycle. The PBP patterns were analyzed by sodium dodecylsulphate polyacrylamide-gel electrophoresis and fluorography. One strain (No. 45 H) has only a single band (mol wt: 27,000) in early log phase, and two additional PBPs of higher mol wt (69,000 and 80,000) in the late log phase. The other strain (No. 2682) possessed two bands with mol wts 27,000 and 38,000 which did not change during its vegetative phase. In strain No. 2682, a new PBP with a mol wt of 58,000 appeared in spore membranes while one of those (mol wt 38,000) present in mycelial membranes disappeared. Our results suggest that appearance of the new PBP in the spore may be associated with the sporulation process. The major PBP band (mol wt: 27,000) present in all stages of the life cycle of these strains, may be characteristic of S. griseus while the other PBPs reflect certain stages of the life cycle. A new method was developed for the production of spore protoplasts by consecutive enzymatic treatments.

The singular continuous diffraction measure of the Thue-Morse chain

The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in $\{\pm 1\}$. We revisit this example and derive a functional equation together with an explicit form of the corresponding singular continuous diffraction measure, which is related to the known representation as a Riesz product.Comment: 6 pages, 1 figure; revised and improved versio