Solitary Metastasis From Cutaneous Melanoma to the Liver: Resection by Extended Left Hepatectomy (Trisegmentectomy) With Clearance of Tumor From the Portal Vein

A 61-year-old woman presented with low grade fever and an epigastric mass eight years following resection of a stage Clark IV infraclavicular cutaneous melanoma followed by axillary node dissection. Investigations revealed a tumor in segment II, III, IV and V of the liver and a thrombus involving the main portal vein. Liver resection with extended left hepatectomy (left trisegmentectomy) and portal vein thrombectomy is reported

A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters

"Squashed Entanglement" - An Additive Entanglement Measure

In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions. We derive certain properties of the new measure which we call "squashed entanglement": it is a lower bound on entanglement of formation and an upper bound on distillable entanglement. Furthermore, it is convex, additive on tensor products, and superadditive in general. Continuity in the state is the only property of our entanglement measure which we cannot provide a proof for. We present some evidence, however, that our quantity has this property, the strongest indication being a conjectured Fannes type inequality for the conditional von Neumann entropy. This inequality is proved in the classical case.Comment: 8 pages, revtex4. v2 has some more references and a bit more discussion, v3 continuity discussion extended, typos correcte

Stability of cluster solutions in a cooperative consumer chain model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.RGC of Hong Kon

Existence and Stability of a Spike in the Central Component for a Consumer Chain Model

We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir

Quantitative analysis of regional distribution of tau pathology with 11C-PBB3-PET in a clinical setting.

PURPOSE The recent developments of tau-positron emission tomography (tau-PET) enable in vivo assessment of neuropathological tau aggregates. Among the tau-specific tracers, the application of 11C-pyridinyl-butadienyl-benzothiazole 3 (11C-PBB3) in PET shows high sensitivity to Alzheimer disease (AD)-related tau deposition. The current study investigates the regional tau load in patients within the AD continuum, biomarker-negative individuals (BN) and patients with suspected non-AD pathophysiology (SNAP) using 11C-PBB3-PET. MATERIALS AND METHODS A total of 23 memory clinic outpatients with recent decline of episodic memory were examined using 11C-PBB3-PET. Pittsburg compound B (11C-PIB) PET was available for 17, 18F-flurodeoxyglucose (18F-FDG) PET for 16, and cerebrospinal fluid (CSF) protein levels for 11 patients. CSF biomarkers were considered abnormal based on Aβ42 ( 450 ng/L). The PET biomarkers were classified as positive or negative using statistical parametric mapping (SPM) analysis and visual assessment. Using the amyloid/tau/neurodegeneration (A/T/N) scheme, patients were grouped as within the AD continuum, SNAP, and BN based on amyloid and neurodegeneration status. The 11C-PBB3 load detected by PET was compared among the groups using both atlas-based and voxel-wise analyses. RESULTS Seven patients were identified as within the AD continuum, 10 SNAP and 6 BN. In voxel-wise analysis, significantly higher 11C-PBB3 binding was observed in the AD continuum group compared to the BN patients in the cingulate gyrus, tempo-parieto-occipital junction and frontal lobe. Compared to the SNAP group, patients within the AD continuum had a considerably increased 11C-PBB3 uptake in the posterior cingulate cortex. There was no significant difference between SNAP and BN groups. The atlas-based analysis supported the outcome of the voxel-wise quantification analysis. CONCLUSION Our results suggest that 11C-PBB3-PET can effectively analyze regional tau load and has the potential to differentiate patients in the AD continuum group from the BN and SNAP group

Faithful Squashed Entanglement

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof is based on two recent results from quantum information theory: the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing. The distance to the set of separable states is measured by the one-way LOCC norm, an operationally-motivated norm giving the optimal probability of distinguishing two bipartite quantum states, each shared by two parties, using any protocol formed by local quantum operations and one-directional classical communication between the parties. A similar result for the Frobenius or Euclidean norm follows immediately. The result has two applications in complexity theory. The first is a quasipolynomial-time algorithm solving the weak membership problem for the set of separable states in one-way LOCC or Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations thereby providing a new characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published version, claims have been weakened from the LOCC norm to the one-way LOCC nor

Genetic Variants of Wnt Transcription Factor TCF-4 (TCF7L2) Putative Promoter Region Are Associated with Small Intestinal Crohn's Disease

Reduced expression of Paneth cell antimicrobial α-defensins, human defensin (HD)-5 and -6, characterizes Crohn's disease (CD) of the ileum. TCF-4 (also named TCF7L2), a Wnt signalling pathway transcription factor, orchestrates Paneth cell differentiation, directly regulates the expression of HD-5 and -6, and was previously associated with the decrease of these antimicrobial peptides in a subset of ileal CD. To investigate a potential genetic association of TCF-4 with ileal CD, we sequenced 2.1 kb of the 5′ flanking region of TCF-4 in a small group of ileal CD patients and controls (n = 10 each). We identified eight single nucleotide polymorphisms (SNPs), of which three (rs3814570, rs10885394, rs10885395) were in linkage disequilibrium and found more frequently in patients; one (rs3814570) was thereby located in a predicted regulatory region. We carried out high-throughput analysis of this SNP in three cohorts of inflammatory bowel disease (IBD) patients and controls. Overall 1399 healthy individuals, 785 ulcerative colitis (UC) patients, 225 CD patients with colonic disease only and 784 CD patients with ileal involvement were used to determine frequency distributions. We found an association of rs3814570 with ileal CD but neither with colonic CD or UC, in a combined analysis (allele positivity: OR 1.27, 95% CI 1.07 to 1.52, p = 0.00737), which was the strongest in ileal CD patients with stricturing behaviour (allele frequency: OR 1.32, 95% CI 1.08 to1.62, p = 0.00686) or an additional involvement of the upper GIT (allele frequency: OR 1.38, 95% CI 1.03 to1.84, p = 0.02882). The newly identified genetic association of TCF-4 with ileal CD provides evidence that the decrease in Paneth cell α-defensins is a primary factor in disease pathogenesis

Lung Volume, Breathing Pattern and Ventilation Inhomogeneity in Preterm and Term Infants

BACKGROUND: Morphological changes in preterm infants with bronchopulmonary dysplasia (BPD) have functional consequences on lung volume, ventilation inhomogeneity and respiratory mechanics. Although some studies have shown lower lung volumes and increased ventilation inhomogeneity in BPD infants, conflicting results exist possibly due to differences in sedation and measurement techniques. METHODOLOGY/PRINCIPAL FINDINGS: We studied 127 infants with BPD, 58 preterm infants without BPD and 239 healthy term-born infants, at a matched post-conceptional age of 44 weeks during quiet natural sleep according to ATS/ERS standards. Lung function parameters measured were functional residual capacity (FRC) and ventilation inhomogeneity by multiple breath washout as well as tidal breathing parameters. Preterm infants with BPD had only marginally lower FRC (21.4 mL/kg) than preterm infants without BPD (23.4 mL/kg) and term-born infants (22.6 mL/kg), though there was no trend with disease severity. They also showed higher respiratory rates and lower ratios of time to peak expiratory flow and expiratory time (t(PTEF)/t(E)) than healthy preterm and term controls. These changes were related to disease severity. No differences were found for ventilation inhomogeneity. CONCLUSIONS: Our results suggest that preterm infants with BPD have a high capacity to maintain functional lung volume during natural sleep. The alterations in breathing pattern with disease severity may reflect presence of adaptive mechanisms to cope with the disease process