On Resource-bounded versions of the van Lambalgen theorem

The van Lambalgen theorem is a surprising result in algorithmic information theory concerning the symmetry of relative randomness. It establishes that for any pair of infinite sequences $A$ and $B$, $B$ is Martin-L\"of random and $A$ is Martin-L\"of random relative to $B$ if and only if the interleaved sequence $A \uplus B$ is Martin-L\"of random. This implies that $A$ is relative random to $B$ if and only if $B$ is random relative to $A$ \cite{vanLambalgen}, \cite{Nies09}, \cite{HirschfeldtBook}. This paper studies the validity of this phenomenon for different notions of time-bounded relative randomness. We prove the classical van Lambalgen theorem using martingales and Kolmogorov compressibility. We establish the failure of relative randomness in these settings, for both time-bounded martingales and time-bounded Kolmogorov complexity. We adapt our classical proofs when applicable to the time-bounded setting, and construct counterexamples when they fail. The mode of failure of the theorem may depend on the notion of time-bounded randomness

Polynomial Time Algorithms for Branching Markov Decision Processes and Probabilistic Min(Max) Polynomial Bellman Equations

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic max(min) polynomial equations, referred to as maxPPSs (and minPPSs, respectively), in time polynomial in both the encoding size of the system of equations and in log(1/epsilon), where epsilon > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We establish this result using a generalization of Newton's method which applies to maxPPSs and minPPSs, even though the underlying functions are only piecewise-differentiable. This generalizes our recent work which provided a P-time algorithm for purely probabilistic PPSs. These equations form the Bellman optimality equations for several important classes of infinite-state Markov Decision Processes (MDPs). Thus, as a corollary, we obtain the first polynomial time algorithms for computing to within arbitrary desired precision the optimal value vector for several classes of infinite-state MDPs which arise as extensions of classic, and heavily studied, purely stochastic processes. These include both the problem of maximizing and mininizing the termination (extinction) probability of multi-type branching MDPs, stochastic context-free MDPs, and 1-exit Recursive MDPs. Furthermore, we also show that we can compute in P-time an epsilon-optimal policy for both maximizing and minimizing branching, context-free, and 1-exit-Recursive MDPs, for any given desired epsilon > 0. This is despite the fact that actually computing optimal strategies is Sqrt-Sum-hard and PosSLP-hard in this setting. We also derive, as an easy consequence of these results, an FNP upper bound on the complexity of computing the value (within arbitrary desired precision) of branching simple stochastic games (BSSGs)

Growing Sugarcane for Energy Use

The increase in energy demand throughout the world, and the rise of greenhouse gas emissions has lead to the exploration of new energy sources. Sugarcane is already being used as a source of energy and is a growing industry. Sugarcane is currently being used to create ethanol and has the potential to be a competitive alternative to fossil fuels if other by-products of the plant are utilized

Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers

The nematic twist-bend (NTB) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase -- the first distinct nematic variant discovered in many years. The NTB phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The NTB structure thus provides another fascinating example of spontaneous chiral symmetry breaking in nature. The order parameter driving the formation of the heliconical state has been theoretically conjectured to be a polarization field, deriving from the bent conformation of the dimers, that rotates helically with the same nanoscale pitch as the director field. It therefore presents a significant challenge for experimental detection. Here we report a second harmonic light scattering (SHLS) study on two achiral, NTB-forming LCs, which is sensitive to the polarization field due to micron-scale distortion of the helical structure associated with naturally-occurring textural defects. These defects are parabolic focal conics of smectic-like ``pseudo-layers", defined by planes of equivalent phase in a coarse-grained description of the NTB state. Our SHLS data are explained by a coarse-grained free energy density that combines a Landau-deGennes expansion of the polarization field, the elastic energy of a nematic, and a linear coupling between the two

Light scattering study of the “pseudo-layer” compression elastic constant in a twist-bend nematic liquid crystal

The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or “pseudo-layers”, each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining “layer” compression and bending ought to be characterized by an effective layer compression elastic constant Beff and average director splay constant Keff1. The magnitude of Keff1 is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, Beff could differ substantially from the typical value of ∼10⁶ Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the “pseudo-layer” structure of the TB phase with Beff in the range 10³–10⁴ Pa. We show additionally that the temperature dependence of Beff at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director

The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games

We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium of G where player 0 wins with probability 1. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if mixed strategies are allowed, decidability remains an open problem. One way to obtain a provably decidable variant of the problem is restricting the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively.Comment: 23 pages; revised versio

The Search for Higher TcT_c in Houston

It is a great pleasure to be invited to join the chorus on this auspicious occasion to celebrate Professor K. Alex Mueller's 90th birthday by Professors Annette Bussman-Holder, Hugo Keller, and Antonio Bianconi. As a student in high temperature superconductivity, I am forever grateful to Professor Alex Mueller and Dr. Georg Bednorz "for their important breakthrough in the discovery of superconductivity in the ceramic materials" in 1986 as described in the citation of their 1987 Nobel Prize in Physics. It is this breakthrough discovery that has ushered in the explosion of research activities in high temperature superconductivity (HTS) and has provided immense excitement in HTS science and technology in the ensuing decades till now. Alex has not been resting on his laurels and has continued to search for the origin of the unusual high temperature superconductivity in cuprates.Comment: Dedicated to Alex Mueller, whose "important breakthrough in the discovery of superconductivity in ceramic materials" in 1986 has changed the world of superconductivit

Population assessment of future trajectories in coronary heart disease mortality.

Background: Coronary heart disease (CHD) mortality rates have been decreasing in Iceland since the 1980s, largely reflecting improvements in cardiovascular risk factors. The purpose of this study was to predict future CHD mortality in Iceland based on potential risk factor trends. Methods and findings: The previously validated IMPACT model was used to predict changes in CHD mortality between 2010 and 2040 among the projected population of Iceland aged 25–74. Calculations were based on combining: i) data on population numbers and projections (Statistics Iceland), ii) population risk factor levels and projections (Refine Reykjavik study), and iii) effectiveness of specific risk factor reductions (published meta-analyses). Projections for three contrasting scenarios were compared: 1) If the historical risk factor trends of past 30 years were to continue, the declining death rates of past decades would level off, reflecting population ageing. 2) If recent trends in risk factors (past 5 years) continue, this would result in a death rate increasing from 49 to 70 per 100,000. This would reflect a recent plateau in previously falling cholesterol levels and recent rapid increases in obesity and diabetes prevalence. 3) Assuming that in 2040 the entire population enjoys optimal risk factor levels observed in low risk cohorts, this would prevent almost all premature CHD deaths before 2040. Conclusions: The potential increase in CHD deaths with recent trends in risk factor levels is alarming both for Iceland and probably for comparable Western populations. However, our results show considerable room for reducing CHD mortality. Achieving the best case scenario could eradicate premature CHD deaths by 2040. Public health policy interventions based on these predictions may provide a cost effective means of reducing CHD mortality in the future

Hybrid Synthetic Receptors on MOSFET Devices for Detection of Prostate Specific Antigen in Human Plasma

The study reports the use of extended gate field-effect transistors (FET) for the label-free and sensitive detection of prostate cancer (PCa) biomarkers in human plasma. The approach integrates for the first time hybrid synthetic receptors comprising of highly selective aptamer-lined pockets (apta-MIP) with FETs for sensitive detection of prostate specific antigen (PSA) at clinically relevant concentrations. The hybrid synthetic receptors were constructed by immobilizing an aptamer–PSA complex on gold and subjecting it to 13 cycles of dopamine electropolymerization. The polymerization resulted in the creation of highly selective polymeric cavities that retained the ability to recognize PSA post removal of the protein. The hybrid synthetic receptors were subsequently used in an extended gate FET setup for electrochemical detection of PSA. The sensor was reported to have a limit of detection of 0.1 pg/mL with a linear detection range from 0.1 pg/mL to 1 ng/mL PSA. Detection of 1–10 pg/mL PSA was also achieved in diluted human plasma. The present apta-MIP sensor developed in conjunction with FET devices demonstrates the potential for clinical application of synthetic hybrid receptors for the detection of clinically relevant biomarkers in complex samples