A generalization of a trace inequality for positive definite matrices

In this note we generalize the trace inequality derived by [1] to the case where the number of terms of the sum (denoted by K) is arbitrary

Power Allocation Games in Wireless Networks of Multi-antenna Terminals

We consider wireless networks that can be modeled by multiple access channels in which all the terminals are equipped with multiple antennas. The propagation model used to account for the effects of transmit and receive antenna correlations is the unitary-invariant-unitary model, which is one of the most general models available in the literature. In this context, we introduce and analyze two resource allocation games. In both games, the mobile stations selfishly choose their power allocation policies in order to maximize their individual uplink transmission rates; in particular they can ignore some specified centralized policies. In the first game considered, the base station implements successive interference cancellation (SIC) and each mobile station chooses his best space-time power allocation scheme; here, a coordination mechanism is used to indicate to the users the order in which the receiver applies SIC. In the second framework, the base station is assumed to implement single-user decoding. For these two games a thorough analysis of the Nash equilibrium is provided: the existence and uniqueness issues are addressed; the corresponding power allocation policies are determined by exploiting random matrix theory; the sum-rate efficiency of the equilibrium is studied analytically in the low and high signal-to-noise ratio regimes and by simulations in more typical scenarios. Simulations show that, in particular, the sum-rate efficiency is high for the type of systems investigated and the performance loss due to the use of the proposed suboptimum coordination mechanism is very small

On the interplay between Babai and Cerny's conjectures

Motivated by the Babai conjecture and the Cerny conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with $n$ states in this class, we prove that the reset thresholds are upper-bounded by $2n^2-6n+5$ and can attain the value $\tfrac{n(n-1)}{2}$. In addition, we study diameters of the pair digraphs of permutation automata and construct $n$-state permutation automata with diameter $\tfrac{n^2}{4} + o(n^2)$.Comment: 21 pages version with full proof

Piecewise semi-ellipsoidal control invariant sets

Computing control invariant sets is paramount in many applications. The families of sets commonly used for computations are ellipsoids and polyhedra. However, searching for a control invariant set over the family of ellipsoids is conservative for systems more complex than unconstrained linear time invariant systems. Moreover, even if the control invariant set may be approximated arbitrarily closely by polyhedra, the complexity of the polyhedra may grow rapidly in certain directions. An attractive generalization of these two families are piecewise semi-ellipsoids. We provide in this paper a convex programming approach for computing control invariant sets of this family.Comment: 7 pages, 3 figures, to be published in IEEE Control Systems Letter

Double Exponential Instability of Triangular Arbitrage Systems

If financial markets displayed the informational efficiency postulated in the efficient markets hypothesis (EMH), arbitrage operations would be self-extinguishing. The present paper considers arbitrage sequences in foreign exchange (FX) markets, in which trading platforms and information are fragmented. In Kozyakin et al. (2010) and Cross et al. (2012) it was shown that sequences of triangular arbitrage operations in FX markets containing 4 currencies and trader-arbitrageurs tend to display periodicity or grow exponentially rather than being self-extinguishing. This paper extends the analysis to 5 or higher-order currency worlds. The key findings are that in a 5-currency world arbitrage sequences may also follow an exponential law as well as display periodicity, but that in higher-order currency worlds a double exponential law may additionally apply. There is an "inheritance of instability" in the higher-order currency worlds. Profitable arbitrage operations are thus endemic rather that displaying the self-extinguishing properties implied by the EMH.Comment: 22 pages, 22 bibliography references, expanded Introduction and Conclusion, added bibliohraphy reference

On the Interplay Between Černý and Babai’s Conjectures

Motivated by the Babai conjecture and the Černý conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with n states in this class, we prove that the reset threshold is upper-bounded by 2n2−6n+5 and can attain the value n(n−1)2. In addition, we study diameters of the pair digraphs of permutation automata and construct n-state permutation automata with diameter n24+o(n2)

Power laws of complex systems from Extreme physical information

Many complex systems obey allometric, or power, laws y=Yx^{a}. Here y is the measured value of some system attribute a, Y is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values +or- n/4, n=0,1,2... Here x is the mass of a randomly selected creature in the population. These quarter-power laws hold for many attributes, such as pulse rate (n=-1). Allometry has, in the past, been theoretically justified on a case-by-case basis. An ultimate goal is to find a common cause for allometry of all types and for both living and nonliving systems. The principle I - J = extrem. of Extreme physical information (EPI) is found to provide such a cause. It describes the flow of Fisher information J => I from an attribute value a on the cell level to its exterior observation y. Data y are formed via a system channel function y = f(x,a), with f(x,a) to be found. Extremizing the difference I - J through variation of f(x,a) results in a general allometric law f(x,a)= y = Yx^{a}. Darwinian evolution is presumed to cause a second extremization of I - J, now with respect to the choice of a. The solution is a=+or-n/4, n=0,1,2..., defining the particular powers of biological allometry. Under special circumstances, the model predicts that such biological systems are controlled by but two distinct intracellular information sources. These sources are conjectured to be cellular DNA and cellular transmembrane ion gradient

A systematic review of patient and health system characteristics associated with late referral in chronic kidney disease

<p>Abstract</p> <p>Background</p> <p>To identify patient and health system characteristics associated with late referral of patients with chronic kidney disease to nephrologists.</p> <p>Methods</p> <p>MEDLINE, CENTRAL, and CINAHL were searched using the appropriate MESH terms in March 2007. Two reviewers individually and in duplicate reviewed the abstracts of 256 articles and selected 18 observational studies for inclusion. The reasons for late referral were categorized into patient or health system characteristics. Data extraction and content appraisal were done using a prespecified protocol.</p> <p>Results</p> <p>Older age, the existence of multiple comorbidities, race other than Caucasian, lack of insurance, lower socioeconomic status and educational levels were patient characteristics associated with late referral of patients with chronic kidney disease. Lack of referring physician knowledge about the appropriate timing of referral, absence of communication between referring physicians and nephrologists, and dialysis care delivered at tertiary medical centers were health system characteristics associated with late referral of patients with chronic kidney disease. Most studies identified multiple factors associated with late referral, although the relative importance and the combined effect of these factors were not systematically evaluated.</p> <p>Conclusion</p> <p>A combination of patient and health system characteristics is associated with late referral of patients with chronic kidney disease. Overall, being older, belonging to a minority group, being less educated, being uninsured, suffering from multiple comorbidities, and the lack of communication between primary care physicians and nephrologists contribute to late referral of patients with chronic kidney disease. Both primary care physicians and nephrologists need to engage in multisectoral collaborative efforts that ensure patient education and enhance physician awareness to improve the care of patients with chronic kidney disease.</p

The evolution of mammalian brain size

Relative brain size has long been considered a reflection of cognitive capacities and has played a fundamental role in developing core theories in the life sciences. Yet, the notion that relative brain size validly represents selection on brain size relies on the untested assumptions that brain-body allometry is restrained to a stable scaling relationship across species and that any deviation from this slope is due to selection on brain size. Using the largest fossil and extant dataset yet assembled, we find that shifts in allometric slope underpin major transitions in mammalian evolution and are often primarily characterized by marked changes in body size. Our results reveal that the largest-brained mammals achieved large relative brain sizes by highly divergent paths. These findings prompt a reevaluation of the traditional paradigm of relative brain size and open new opportunities to improve our understanding of the genetic and developmental mechanisms that influence brain size

Listeners feel the beat: Entrainment to English and French speech rhythms

Can listeners entrain to speech rhythms? Monolingual speakers of English and French and balanced English–French bilinguals tapped along with the beat they perceived in sentences spoken in a stress-timed language, English, and a syllable-timed language, French. All groups of participants tapped more regularly to English than to French utterances. Tapping performance was also influenced by the participants’ native language: English-speaking participants and bilinguals tapped more regularly and at higher metrical levels than did French-speaking participants, suggesting that long-term linguistic experience with a stress-timed language can differentiate speakers’ entrainment to speech rhythm