The unfolded protein response (UPR) is a transcriptional and translational intracellular signaling pathway activated by the accumulation of unfolded proteins in the lumen of the endoplasmic reticulum (ER). We have used C. elegans as a genetic model system to dissect UPR signaling in a multicellular organism. C. elegans requires ire-1-mediated splicing of xbp-1 mRNA for UPR gene transcription and survival upon ER stress. In addition, ire-1/xbp-1 acts with pek-1, a protein kinase that mediates translation attenuation, in complementary pathways that are essential for worm development and survival. We propose that UPR transcriptional activation by ire-1 as well as translational attenuation by pek-1 maintain ER homeostasis. The results demonstrate that the UPR and ER homeostasis are essential for metazoan development.

Sufficient conditions for complete controllability of N-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic oscillator systems, as well as some systems with degenerate energy levels. Controllability of these model systems is of special interest since they have many applications in physics, e.g., Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.

We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic XXZ model, and the ferromagnetic XXZ model with anisotropy parameter ∆ ≥ 1. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the magnetic field can induce entanglement in the antiferromagnetic XXX model, but cannot induce entanglement in the ferromagnetic XXX model.

Background: The four highly homologous human EHD proteins (EHD1-4) form a distinct subfamily of the Eps15 homology domain-containing protein family and are thought to regulate endocytic recycling. Certain members of this family have been studied in different cellular contexts; however, a lack of concurrent analyses of all four proteins has impeded an appreciation of their redundant versus distinct functions.

We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling numbers enumerating partitions of a set. This framework reveals several inherent relations between ordering problems and combinatorial objects, and displays the analytical background to Wick's theorem. The methodology can be straightforwardly generalized from the simple example given herein to a wide class of operators.

The molecular mechanisms that enable multicellular organisms to sense and modulate their responses to hyperosmotic environments are poorly understood. Here, we employ Caenorhabditis elegans to characterize the response of a multicellular organism to osmotic stress and establish a genetic screen to isolate mutants that are osmotic stress resistant (OSR). In this study, we describe the cloning of a novel gene, osr-1, and demonstrate that it regulates osmosensation, adaptation, and survival in hyperosmotic environments. Whereas wild-type animals exposed to hyperosmotic conditions rapidly lose body volume, motility, and viability, osr-1(rm1) mutant animals maintain normal body volume, motility, and viability even upon chronic exposures to high osmolarity environments. In addition, osr-1(rm1) animals are specifically resistant to osmotic stress and are distinct from previously characterized osmotic avoidance defective (OSM) and general stress resistance age-1(hx546) mutants. OSR-1 is expressed in the hypodermis and intestine, and expression of OSR-1 in hypodermal cells rescues the osr-1(rm1) phenotypes. Genetic epistasis analysis indicates that OSR-1 regulates survival under osmotic stress via CaMKII and a conserved p38 MAP kinase signaling cascade and regulates osmotic avoidance and resistance to acute dehydration likely by distinct mechanisms. We suggest that OSR-1 plays a central role in integrating stress detection and adaptation responses by invoking multiple signaling pathways to promote survival under hyperosmotic environments.

We solve the boson normal ordering problem for F (a † ) r a s , with r, s positive integers, a, a † = 1, i.e. we provide exact and explicit expressions for its normal form N F (a † ) r a s , where in N (F ) all a's are to the right. The solution involves integer sequences of numbers which are generalizations of the conventional Bell and Stirling numbers whose values they assume for r = s = 1. A comprehensive theory of such generalized combinatorial numbers is given including closed-form expressions (extended Dobinski -type formulas) and generating functions. These last are special expectation values in boson coherent states. Consider a function F (x) having a Taylor expansion aroundIn this note we will collect the formulas concerning our solution of the normal ordering problem for F (a † ) r a s , where a, a † are the boson annihilation and creation operators, a, a † = 1, and r and s are positive integers. The normally ordered form of the operator, where in N (F ) all the a's are to the right. It satisfies the operator identity:Furthermore, an auxiliary symbol : O(a, a † ) : will be used, which means expand O in powers of a and a † and order normally assuming they commute [1], [2].The combinatorial numbers S(n, k), known as Stirling numbers of the second kind, and their sums B(n), the Bell numbers, arise naturally in the normal ordering procedure for r = s = 1, as follows [3]:which may be taken as definitions of S(n, k) and B(n). In the present work we shall treat the case of general (r, s), consequently generalizing these combinatorial numbers.For the moment we restrict ourselves to the case r ≥ s, the other alternative being treated later. We do not give the proofs of the formulas here; they will be given elsewhere [4]. The case r = s = 1 is known [1], [2] and some features of the r > 1, s = 1 case have been published [5]. When needed we shall refer to [1], [2] and [5] where particular cases of our more general formulas are discussed.We define the set of positive integers S r,s (n, k) entering the expansion:(a † ) r a s n = N (a † ) r a s n = (a † )n(r−s) ns k=s S r,s (n, k)(a † ) k a

Abstract. Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we investigate the question of complete controllability for finite-level quantum systems subject to a single control field, for which the interaction is of dipole form. Sufficient criteria for complete controllability of a wide range of finite-level quantum systems are established and the question of limits of complete controllability is addressed. Finally, the results are applied to give a classification of complete controllability for four-level systems.