The asymmetric sandwich theorem

We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.Comment: 17 page

Prevalence of qacA/B genes and mupirocin resistance among methicillin-resistant Staphylococcus aureus (MRSA) isolates in the setting of chlorhexidine bathing without mupirocin

OBJECTIVE: We aimed to determine the frequency of qacA/B chlorhexidine tolerance genes and high-level mupirocin resistance among MRSA isolates before and after the introduction of a chlorhexidine (CHG) daily bathing intervention in a surgical intensive care unit (SICU). DESIGN: Retrospective cohort study (2005–2012) SETTING: A large tertiary-care center PATIENTS: Patients admitted to SICU who had MRSA surveillance cultures of the anterior nares METHODS: A random sample of banked MRSA anterior nares isolates recovered during (2005) and after (2006–2012) implementation of a daily CHG bathing protocol was examined for qacA/B genes and high-level mupirocin resistance. Staphylococcal cassette chromosome mec (SCCmec) typing was also performed. RESULTS: Of the 504 randomly selected isolates (63 per year), 36 (7.1%) were qacA/B positive ( + ) and 35 (6.9%) were mupirocin resistant. Of these, 184 (36.5%) isolates were SCCmec type IV. There was a significant trend for increasing qacA/B (P= .02; highest prevalence, 16.9% in 2009 and 2010) and SCCmec type IV (P< .001; highest prevalence, 52.4% in 2012) during the study period. qacA/B( + ) MRSA isolates were more likely to be mupirocin resistant (9 of 36 [25%] qacA/B( + ) vs 26 of 468 [5.6%] qacA/B(−); P= .003). CONCLUSIONS: A long-term, daily CHG bathing protocol was associated with a change in the frequency of qacA/B genes in MRSA isolates recovered from the anterior nares over an 8-year period. This change in the frequency of qacA/B genes is most likely due to patients in those years being exposed in prior admissions. Future studies need to further evaluate the implications of universal CHG daily bathing on MRSA qacA/B genes among hospitalized patients

A stochastic flow rule for granular materials

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials - discreteness and randomness - via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along slip-lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction. In the continuum limit (based on a Fokker-Planck equation for the spot concentration), this simple model is able to predict a variety of granular flow profiles in flat-bottom silos, annular Couette cells, flowing heaps, and plate-dragging experiments -- with essentially no fitting parameters -- although it is only expected to function where material is at incipient failure and slip-lines are inadmissible. For special cases of admissible slip-lines, such as plate dragging under a heavy load or flow down an inclined plane, we postulate a transition to rate-dependent Bagnold rheology, where flow occurs by sliding shear planes. With different yield criteria, the SFR provides a general framework for multiscale modeling of plasticity in amorphous materials, cycling between continuum limit-state stress calculations, meso-scale spot random walks, and microscopic particle relaxation

Glutamate-mediated blood-brain barrier opening. implications for neuroprotection and drug delivery

The blood-brain barrier is a highly selective anatomical and functional interface allowing a unique environment for neuro-glia networks. Blood-brain barrier dysfunction is common in most brain disorders and is associated with disease course and delayed complications. However, the mechanisms underlying blood-brain barrier opening are poorly understood. Here we demonstrate the role of the neurotransmitter glutamate in modulating early barrier permeability in vivo Using intravital microscopy, we show that recurrent seizures and the associated excessive glutamate release lead to increased vascular permeability in the rat cerebral cortex, through activation of NMDA receptors. NMDA receptor antagonists reduce barrier permeability in the peri-ischemic brain, whereas neuronal activation using high-intensity magnetic stimulation increases barrier permeability and facilitates drug delivery. Finally, we conducted a double-blind clinical trial in patients with malignant glial tumors, using contrast-enhanced magnetic resonance imaging to quantitatively assess blood-brain barrier permeability. We demonstrate the safety of stimulation that efficiently increased blood-brain barrier permeability in 10 of 15 patients with malignant glial tumors. We suggest a novel mechanism for the bidirectional modulation of brain vascular permeability toward increased drug delivery and prevention of delayed complications in brain disorders. SIGNIFICANCE STATEMENT: In this study, we reveal a new mechanism that governs blood-brain barrier (BBB) function in the rat cerebral cortex, and, by using the discovered mechanism, we demonstrate bidirectional control over brain endothelial permeability. Obviously, the clinical potential of manipulating BBB permeability for neuroprotection and drug delivery is immense, as we show in preclinical and proof-of-concept clinical studies. This study addresses an unmet need to induce transient BBB opening for drug delivery in patients with malignant brain tumors and effectively facilitate BBB closure in neurological disorders

Tensile Fracture of Welded Polymer Interfaces: Miscibility, Entanglements and Crazing

Large-scale molecular simulations are performed to investigate tensile failure of polymer interfaces as a function of welding time $t$. Changes in the tensile stress, mode of failure and interfacial fracture energy $G_I$ are correlated to changes in the interfacial entanglements as determined from Primitive Path Analysis. Bulk polymers fail through craze formation, followed by craze breakdown through chain scission. At small $t$ welded interfaces are not strong enough to support craze formation and fail at small strains through chain pullout at the interface. Once chains have formed an average of about one entanglement across the interface, a stable craze is formed throughout the sample. The failure stress of the craze rises with welding time and the mode of craze breakdown changes from chain pullout to chain scission as the interface approaches bulk strength. The interfacial fracture energy $G_I$ is calculated by coupling the simulation results to a continuum fracture mechanics model. As in experiment, $G_I$ increases as $t^{1/2}$ before saturating at the average bulk fracture energy $G_b$. As in previous simulations of shear strength, saturation coincides with the recovery of the bulk entanglement density. Before saturation, $G_I$ is proportional to the areal density of interfacial entanglements. Immiscibiltiy limits interdiffusion and thus suppresses entanglements at the interface. Even small degrees of immisciblity reduce interfacial entanglements enough that failure occurs by chain pullout and $G_I \ll G_b$

Liesegang patterns: Effect of dissociation of the invading electrolyte

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1+p, that characterizes the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing dissociation constant, K_d. Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K_d dependence of 1+p.Comment: RevTex, 8 pages, 3 eps figure

Drift and Diffusion in Periodically Driven Renewal Processes

We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show that the growth of the cumulants of the number of events is asymptotically periodic and develop a theory which relates these periodic growth coefficients to the waiting time distribution defining the periodic renewal process. The first two coefficients, which are the mean frequency and effective diffusion coefficient of the number of events are considered in greater detail. They may be used to quantify stochastic synchronization.Comment: 29 pages, 6 figures, submitted to Journal of Statistical Physic

Stochastic resonance in a non Markovian discrete state model for excitable systems

We study a non Markovian three state model, subjected to an external periodic signal. This model is intended to describe an excitable systems with periodical driving. In the limit of a small amplitude of the external signal we derive expressions for the spectral power amplification and the signal to noise ratio as well as for the inter-spike interval distribution.Comment: 5 pages, 3 figure

Band Formation during Gaseous Diffusion in Aerogels

We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides of and react in silica aerogel rods with porosity of 92 % and average pore size of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin sheet-like structures. We present a numerical study of the phenomenon. Due to the difference in boundary conditions between this system and those usually studied, we find the sheet-like structures in the aerogel to differ significantly from older studies. The influence of random nucleation centers and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on request from author