Bounds on Dimension Reduction in the Nuclear Norm

$\newcommand{\schs}{\scriptstyle{\mathsf{S}}_1}$For all $n \ge 1$, we give an explicit construction of $m \times m$ matrices $A_1,\ldots,A_n$ with $m = 2^{\lfloor n/2 \rfloor}$ such that for any $d$ and $d \times d$ matrices $A'_1,\ldots,A'_n$ that satisfy \|A'_i-A'_j\|_{\schs} \,\leq\, \|A_i-A_j\|_{\schs}\,\leq\, (1+\delta) \|A'_i-A'_j\|_{\schs} for all $i,j\in\{1,\ldots,n\}$ and small enough $\delta = O(n^{-c})$, where $c> 0$ is a universal constant, it must be the case that $d \ge 2^{\lfloor n/2\rfloor -1}$. This stands in contrast to the metric theory of commutative $\ell_p$ spaces, as it is known that for any $p\geq 1$, any $n$ points in $\ell_p$ embed exactly in $\ell_p^d$ for $d=n(n-1)/2$. Our proof is based on matrices derived from a representation of the Clifford algebra generated by $n$ anti-commuting Hermitian matrices that square to identity, and borrows ideas from the analysis of nonlocal games in quantum information theory.Comment: 16 page

Bounds on Dimension Reduction in the Nuclear Norm

For all n ≥ 1, we give an explicit construction of m × m matrices A_1,…,A_n with m = 2^([n/2]) such that for any d and d × d matrices A′_1,…,A′_n that satisfy ∥A_′i−A′_j∥S_1 ≤ ∥A_i−A_j∥S_1 ≤ (1+δ)∥A′_i−A′_j∥S_1 for all i,j∈{1,…,n} and small enough δ = O(n^(−c)), where c > 0 is a universal constant, it must be the case that d ≥ 2^([n/2]−1). This stands in contrast to the metric theory of commutative ℓ_p spaces, as it is known that for any p ≥ 1, any n points in ℓ_p embed exactly in ℓ^d_p for d = n(n−1)/2. Our proof is based on matrices derived from a representation of the Clifford algebra generated by n anti-commuting Hermitian matrices that square to identity, and borrows ideas from the analysis of nonlocal games in quantum information theory

Optimal networks for Quantum Metrology: semidefinite programs and product rules

We investigate the optimal estimation of a quantum process that can possibly consist of multiple time steps. The estimation is implemented by a quantum network that interacts with the process by sending an input and processing the output at each time step. We formulate the search of the optimal network as a semidefinite program and use duality theory to give an alternative expression for the maximum payoff achieved by estimation. Combining this formulation with a technique devised by Mittal and Szegedy we prove a general product rule for the joint estimation of independent processes, stating that the optimal joint estimation can achieved by estimating each process independently, whenever the figure of merit is of a product form. We illustrate the result in several examples and exhibit counterexamples showing that the optimal joint network may not be the product of the optimal individual networks if the processes are not independent or if the figure of merit is not of the product form. In particular, we show that entanglement can reduce by a factor K the variance in the estimation of the sum of K independent phase shifts.Comment: 19 pages, no figures, published versio

The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

A channel-based framework for steering, non-locality and beyond

Non-locality and steering are both non-classical phenomena witnessed in nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, 'post-quantum steering' has been described, which is steering that cannot be reproduced by measurements on entangled states but does not lead to superluminal signalling. In this work we present a framework based on the study of quantum channels in which one can study steering (and non-locality) in quantum theory and beyond. In this framework, we show that kinds of steering, whether quantum or post-quantum, are directly related to particular families of quantum channels that have been previously introduced by Beckman et al (2001 Phys. Rev. A 64 052309). Utilizing this connection we also demonstrate new analytical examples of post-quantum steering, give a quantum channel interpretation of almost quantum non-locality and steering, easily recover and generalize the celebrated Gisin–Hughston–Jozsa–Wootters theorem, and initiate the study of post-quantum Buscemi non-locality and non-classical teleportation. In this way, we see post-quantum non-locality and steering as just two aspects of a more general phenomenon

Thrombocytopenia in the experimental leptospirosis of guinea pig is not related to disseminated intravascular coagulation

BACKGROUND: Thrombocytopenia is commonly observed in severe leptospirosis. However, previous studies on coagulation alterations during leptospirosis resulted in inconsistent conclusions. Some findings showed that the prominent levels of thrombocytopenia observed in severe leptospirosis did not reflect the occurrence of disseminated intravascular coagulation (DIC) syndrome, while the others reached the conclusion that the hemorrhages observed in leptospirosis were due to DIC. The aim of this study is to elucidate whether DIC is an important feature of leptospirosis. METHODS: The leptospirosis model of guinea pig was established by intraperitoneal inoculation of Leptospira interrogans strain Lai. Hematoxylin and eosin (HE) staining, electron microscopy and immunohistochemistry staining were used to detect the pathologic changes. Platelet thrombus or fibrin thrombus was detected by HE, Martius Scarlet Blue (MSB) staining and electron microscopy. Hemostatic molecular markers such as 11-dehydrogenate thromboxane B2 (11-DH-TXB2), thrombomodulin (TM), thrombin-antithrombin III complex (TAT), D-Dimer and fibrin (ogen) degradation products (FDPs) in the plasma were examined by quantitative enzyme-linked immunosorbent assay (ELISA) to evaluate the hematological coagulative alterations in leptospirosis models. RESULTS: Pulmonary hemorrhage appeared in the model guinea pig 24 hours after leptospires intraperitoneal inoculation, progressing to a peak at 96 hours after the infection. Leptospires were detected 24 hours post-inoculation in the liver, 48 hours in the lung and 72 hours in the kidney by immunohistochemistry staining. Spiral form of the bacteria was initially observed in the liver, lung and kidney suggestive of intact leptospires, granular form of leptospires was seen as the severity increased. Platelet aggregation in hepatic sinusoid as well as phagocytosis of erythrocytes and platelets by Kupffer cells were both observed. Neither platelet thrombus nor fibrin thrombus was found in the liver, lung or kidney via morphological observation. Thrombocytopenia was observed in all infected guinea pigs of our experimental leptospirosis study. Analysis of hematologic molecular markers showed that 11-DH-TXB2 and TM in the plasma were elevated significantly. TAT that reflects the thrombin activation had a trend of decline after infection. Although D-dimer and FDPs increased statistically, the increasing may not bear clinical significance. CONCLUSION: Pathologic and hematological studies for experimental leptospirosis of guinea pig indicated that the thrombocytopenia found in guinea pigs did not correlate with the occurrence of DIC. The platelet aggregation and Kupffer cells phagocytosis might be the potential causes of thrombocytopenia in severe leptospirosis

The Urokinase Receptor (uPAR) Facilitates Clearance of Borrelia burgdorferi

The causative agent of Lyme borreliosis, the spirochete Borrelia burgdorferi, has been shown to induce expression of the urokinase receptor (uPAR); however, the role of uPAR in the immune response against Borrelia has never been investigated. uPAR not only acts as a proteinase receptor, but can also, dependently or independently of ligation to uPA, directly affect leukocyte function. We here demonstrate that uPAR is upregulated on murine and human leukocytes upon exposure to B. burgdorferi both in vitro as well as in vivo. Notably, B. burgdorferi-inoculated C57BL/6 uPAR knock-out mice harbored significantly higher Borrelia numbers compared to WT controls. This was associated with impaired phagocytotic capacity of B. burgdorferi by uPAR knock-out leukocytes in vitro. B. burgdorferi numbers in vivo, and phagocytotic capacity in vitro, were unaltered in uPA, tPA (low fibrinolytic activity) and PAI-1 (high fibrinolytic activity) knock-out mice compared to WT controls. Strikingly, in uPAR knock-out mice partially backcrossed to a B. burgdorferi susceptible C3H/HeN background, higher B. burgdorferi numbers were associated with more severe carditis and increased local TLR2 and IL-1β mRNA expression. In conclusion, in B. burgdorferi infection, uPAR is required for phagocytosis and adequate eradication of the spirochete from the heart by a mechanism that is independent of binding of uPAR to uPA or its role in the fibrinolytic system

Alterations in the human lung proteome with lipopolysaccharide

<p>Abstract</p> <p>Background</p> <p>Recombinant human activated protein C (rhAPC) is associated with improved survival in high-risk patients with severe sepsis; however, the effects of both lipopolysaccharide (LPS) and rhAPC on the bronchoalveolar lavage fluid (BALF) proteome are unknown.</p> <p>Methods</p> <p>Using differential in gel electrophoresis (DIGE) we identified changes in the BALF proteome from 10 healthy volunteers given intrapulmonary LPS in one lobe and saline in another lobe. Subjects were randomized to pretreatment with saline or rhAPC.</p> <p>Results</p> <p>An average of 255 protein spots were detected in each proteome. We found 31 spots corresponding to 8 proteins that displayed abundance increased or decreased at least 2-fold after LPS. Proteins that decreased after LPS included surfactant protein A, immunoglobulin J chain, fibrinogen-γ, α₁-antitrypsin, immunoglobulin, and α₂-HS-glycoprotein. Haptoglobin increased after LPS-treatment. Treatment with rhAPC was associated with a larger relative decrease in immunoglobulin J chain, fibrinogen-γ, α₁-antitrypsin, and α₂-HS-glycoprotein.</p> <p>Conclusion</p> <p>Intrapulmonary LPS was associated with specific protein changes suggesting that the lung response to LPS is more than just a loss of integrity in the alveolar epithelial barrier; however, pretreatment with rhAPC resulted in minor changes in relative BALF protein abundance consistent with its lack of affect in ALI and milder forms of sepsis.</p

Network Topologies and Dynamics Leading to Endotoxin Tolerance and Priming in Innate Immune Cells

The innate immune system, acting as the first line of host defense, senses and adapts to foreign challenges through complex intracellular and intercellular signaling networks. Endotoxin tolerance and priming elicited by macrophages are classic examples of the complex adaptation of innate immune cells. Upon repetitive exposures to different doses of bacterial endotoxin (lipopolysaccharide) or other stimulants, macrophages show either suppressed or augmented inflammatory responses compared to a single exposure to the stimulant. Endotoxin tolerance and priming are critically involved in both immune homeostasis and the pathogenesis of diverse inflammatory diseases. However, the underlying molecular mechanisms are not well understood. By means of a computational search through the parameter space of a coarse-grained three-node network with a two-stage Metropolis sampling approach, we enumerated all the network topologies that can generate priming or tolerance. We discovered three major mechanisms for priming (pathway synergy, suppressor deactivation, activator induction) and one for tolerance (inhibitor persistence). These results not only explain existing experimental observations, but also reveal intriguing test scenarios for future experimental studies to clarify mechanisms of endotoxin priming and tolerance.Comment: 15 pages, 8 figures, submitte