Derivatives of Entropy Rate in Special Families of Hidden Markov Chains

Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise. Namely, they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time. We generalize this result to a natural class of hidden Markov chains called ``Black Holes.'' We also discuss in depth special cases of binary Markov chains observed in binary symmetric noise, and give an abstract formula for the first derivative in terms of a measure on the simplex due to Blackwell.Comment: The relaxed condtions for entropy rate and examples are taken out (to be part of another paper). The section about general principle and an example to determine the domain of analyticity is taken out (to be part of another paper). A section about binary Markov chains corrupted by binary symmetric noise is adde

Entanglement area law from specific heat capacity

We study the scaling of entanglement in low-energy states of quantum many-body models on lattices of arbitrary dimensions. We allow for unbounded Hamiltonians such that systems with bosonic degrees of freedom are included. We show that if at low enough temperatures the specific heat capacity of the model decays exponentially with inverse temperature, the entanglement in every low-energy state satisfies an area law (with a logarithmic correction). This behaviour of the heat capacity is typically observed in gapped systems. Assuming merely that the low-temperature specific heat decays polynomially with temperature, we find a subvolume scaling of entanglement. Our results give experimentally verifiable conditions for area laws, show that they are a generic property of low-energy states of matter, and, to the best of our knowledge, constitute the first proof of an area law for unbounded Hamiltonians beyond those that are integrable.Comment: v3 now featuring bosonic system

Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems

We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of $N$ spins arranged on a $d$-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to $O(N^{1/(d+1)})$ spins. The proof rests on a variant of the Berry--Esseen theorem for quantum lattice systems and ideas from quantum information theory

Finite element analysis of fluid-filled elastic piping systems

Two finite element procedures are described for predicting the dynamic response of general 3-D fluid-filled elastic piping systems. The first approach, a low frequency procedure, models each straight pipe or elbow as a sequence of beams. The contained fluid is modeled as a separate coincident sequence axial members (rods) which are tied to the pipe in the lateral direction. The model includes the pipe hoop strain correction to the fluid sound speed and the flexibility factor correction to the elbow flexibility. The second modeling approach, an intermediate frequency procedure, follows generally the original Zienkiewicz-Newton scheme for coupled fluid-structure problems except that the velocity potential is used as the fundamental fluid unknown to symmetrize the coefficient matrices. From comparisons of the beam model predictions to both experimental data and the 3-D model, the beam model is validated for frequencies up to about two-thirds of the lowest fluid-filled labor pipe mode. Accurate elbow flexibility factors are seen to be crucial for effective beam modeling of piping systems

The dynamic analysis of submerged structures

Methods are described by which the dynamic interaction of structures with surrounding fluids can be computed by using finite element techniques. In all cases, the fluid is assumed to behave as an acoustic medium and is initially stationary. Such problems are solved either by explicitly modeling the fluid (using pressure or displacement as the basic fluid unknown) or by using decoupling approximations which take account of the fluid effects without actually modeling the fluid

Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum lattices. In a first step, we show that states with exponentially decaying correlations equilibrate after a quantum quench. Then we show that the equilibrium state is locally equivalent to a thermal state, provided that the free energy of the equilibrium state is sufficiently small and the thermal state has exponentially decaying correlations. As an application, we look at a related important question: When are thermal states stable against noise? In other words, if we locally disturb a closed quantum system in a thermal state, will it return to thermal equilibrium? We rigorously show that this occurs when the correlations in the thermal state are exponentially decaying. All our results come with finite-size bounds, which are crucial for the growing field of quantum thermodynamics and other physical applications.Comment: 8 pages (5 for main text and 3 for appendices); v2 is essentially the published versio

Determining how atmospheric carbon dioxide concentrations have changed during the history of the Earth

The reconstruction of ancient atmospheric carbon dioxide concentrations is essential to understanding the history of the Earth and life. It is also an important guide to identifying the sensitivity of the Earth system to this greenhouse gas and, therefore, constraining its future impact on climate. However, determining the concentration of CO2 in ancient atmospheres is a challenging endeavour requiring the application of state-of-the-art analytical chemistry to geological materials, underpinned by an understanding of photosynthesis and biochemistry. It is truly an interdisciplinary challenge

Advances in Kriging-Based Autonomous X-Ray Scattering Experiments.

Autonomous experimentation is an emerging paradigm for scientific discovery, wherein measurement instruments are augmented with decision-making algorithms, allowing them to autonomously explore parameter spaces of interest. We have recently demonstrated a generalized approach to autonomous experimental control, based on generating a surrogate model to interpolate experimental data, and a corresponding uncertainty model, which are computed using a Gaussian process regression known as ordinary Kriging (OK). We demonstrated the successful application of this method to exploring materials science problems using x-ray scattering measurements at a synchrotron beamline. Here, we report several improvements to this methodology that overcome limitations of traditional Kriging methods. The variogram underlying OK is global and thus insensitive to local data variation. We augment the Kriging variance with model-based measures, for instance providing local sensitivity by including the gradient of the surrogate model. As with most statistical regression methods, OK minimizes the number of measurements required to achieve a particular model quality. However, in practice this may not be the most stringent experimental constraint; e.g. the goal may instead be to minimize experiment duration or material usage. We define an adaptive cost function, allowing the autonomous method to balance information gain against measured experimental cost. We provide synthetic and experimental demonstrations, validating that this improved algorithm yields more efficient autonomous data collection

A central role for C1q/TNF-related protein 13 (CTRP13) in modulating food intake and body weight.

C1q/TNF-related protein 13 (CTRP13), a hormone secreted by adipose tissue (adipokines), helps regulate glucose metabolism in peripheral tissues. We previously reported that CTRP13 expression is increased in obese and hyperphagic leptin-deficient mice, suggesting that it may modulate food intake and body weight. CTRP13 is also expressed in the brain, although its role in modulating whole-body energy balance remains unknown. Here, we show that CTRP13 is a novel anorexigenic factor in the mouse brain. Quantitative PCR demonstrated that food restriction downregulates Ctrp13 expression in mouse hypothalamus, while high-fat feeding upregulates expression. Central administration of recombinant CTRP13 suppressed food intake and reduced body weight in mice. Further, CTRP13 and the orexigenic neuropeptide agouti-related protein (AgRP) reciprocally regulate each other's expression in the hypothalamus: central delivery of CTRP13 suppressed Agrp expression, while delivery of AgRP increased Ctrp13 expression. Food restriction alone reduced Ctrp13 and increased orexigenic neuropeptide gene (Npy and Agrp) expression in the hypothalamus; in contrast, when food restriction was coupled to enhanced physical activity in an activity-based anorexia (ABA) mouse model, hypothalamic expression of both Ctrp13 and Agrp were upregulated. Taken together, these results suggest that CTRP13 and AgRP form a hypothalamic feedback loop to modulate food intake and that this neural circuit may be disrupted in an anorexic-like condition