On the dual nature of partial theta functions and Appell-Lerch sums

In recent work, Hickerson and the author demonstrated that it is useful to think of Appell--Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell--Lerch sums. In this sense, Appell--Lerch sums and partial theta functions appear to be dual to each other. This duality theory is not unlike that found by Andrews between various sets of identities of Rogers-Ramanujan type with respect to Baxter's solution to the hard hexagon model of statistical mechanics. As an application we construct bilateral $q$-series with mixed mock modular behaviour.Comment: To be published in Advances in Mathematic

Hecke-type double sums, Appell-Lerch sums, and mock theta functions (I)

By developing a connection between partial theta functions and Appell-Lerch sums, we find and prove a formula which expresses Hecke-type double sums in terms of Appell-Lerch sums and theta functions. Not only does our formula prove classical Hecke-type double sum identities such as those found in work Kac and Peterson on affine Lie Algebras and Hecke modular forms, but once we have the Hecke-type forms for Ramanujan's mock theta functions our formula gives straightforward proofs of many of the classical mock theta function identities. In particular, we obtain a new proof of the mock theta conjectures. Our formula also applies to positive-level string functions associated with admissable representations of the affine Lie Algebra $A_1^{(1)}$ as introduced by Kac and Wakimoto

Coulomb Gaps in One-Dimensional Spin-Polarized Electron Systems

We investigate the density of states (DOS) near the Fermi energy of one-dimensional spin-polarized electron systems in the quantum regime where the localization length is comparable to or larger than the inter-particle distance. The Wigner lattice gap of such a system, in the presence of weak disorder, can occur precisely at the Fermi energy, coinciding with the Coulomb gap in position. The interplay between the two is investigated by treating the long-range Coulomb interaction and the random disorder potential in a self-consistent Hartree-Fock approximation. The DOS near the Fermi energy is found to be well described by a power law whose exponent decreases with increasing disorder strength.Comment: 4 pages, revtex, 4 figures, to be published in Phys. Rev. B as a Rapid Communicatio

CT-based lung motion differences in patients with usual interstitial pneumonia and nonspecific interstitial pneumonia

We applied quantitative CT image matching to assess the degree of motion in the idiopathic ILD such as usual interstitial pneumonia (UIP) and nonspecific interstitial pneumonia (NSIP). Twenty-one normal subjects and 42 idiopathic ILD (31 UIP and 11 NSIP) patients were retrospectively included. Inspiratory and expiratory CT images, reviewed by two experienced radiologists, were used to compute displacement vectors at local lung regions matched by image registration. Normalized three-dimensional and two-dimensional (dorsal-basal) displacements were computed at a sub-acinar scale. Displacements, volume changes, and tissue fractions in the whole lung and the lobes were compared between normal, UIP, and NSIP subjects. The dorsal-basal displacement in lower lobes was smaller in UIP patients than in NSIP or normal subjects (p = 0.03, p = 0.04). UIP and NSIP were not differentiated by volume changes in the whole lung or upper and lower lobes (p = 0.53, p = 0.12, p = 0.97), whereas the lower lobe air volume change was smaller in both UIP and NSIP than normal subjects (p = 0.02, p = 0.001). Regional expiratory tissue fractions and displacements showed positive correlations in normal and UIP subjects but not in NSIP subjects. In summary, lung motionography quantified by image registration-based lower lobe dorsal-basal displacement may be used to assess the degree of motion, reflecting limited motion due to fibrosis in the ILD such as UIP and NSIP

DNA Checkpoint and Repair Factors Are Nuclear Sensors for Intracellular Organelle Stresses-Inflammations and Cancers Can Have High Genomic Risks.

Under inflammatory conditions, inflammatory cells release reactive oxygen species (ROS) and reactive nitrogen species (RNS) which cause DNA damage. If not appropriately repaired, DNA damage leads to gene mutations and genomic instability. DNA damage checkpoint factors (DDCF) and DNA damage repair factors (DDRF) play a vital role in maintaining genomic integrity. However, how DDCFs and DDRFs are modulated under physiological and pathological conditions are not fully known. We took an experimental database analysis to determine the expression of 26 DNA D

Characterization of soluble bromide measurements and a case study of BrO observations during ARCTAS

A focus of the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) mission was examination of bromine photochemistry in the spring time high latitude troposphere based on aircraft and satellite measurements of bromine oxide (BrO) and related species. The NASA DC-8 aircraft utilized a chemical ionization mass spectrometer (CIMS) to measure BrO and a mist chamber (MC) to measure soluble bromide. We have determined that the MC detection efficiency to molecular bromine (Br2), hypobromous acid (HOBr), bromine oxide (BrO), and hydrogen bromide (HBr) as soluble bromide (Br−) was 0.9±0.1, 1.06+0.30/−0.35, 0.4±0.1, and 0.95±0.1, respectively. These efficiency factors were used to estimate soluble bromide levels along the DC-8 flight track of 17 April 2008 from photochemical calculations constrained to in situ BrO measured by CIMS. During this flight, the highest levels of soluble bromide and BrO were observed and atmospheric conditions were ideal for the space-borne observation of BrO. The good agreement (R2 = 0.76; slope = 0.95; intercept = −3.4 pmol mol−1) between modeled and observed soluble bromide, when BrO was above detection limit (\u3e2 pmol mol−1) under unpolluted conditions (NOmol−1), indicates that the CIMS BrO measurements were consistent with the MC soluble bromide and that a well characterized MC can be used to derive mixing ratios of some reactive bromine compounds. Tropospheric BrO vertical column densities (BrOVCD) derived from CIMS BrO observations compare well with BrOTROPVCD from OMI on 17 April 2008

Overt ischemic colitis after endovascular repair of aortoiliac aneurysms

AbstractObjectiveControversy exists as to the cause of ischemic colitis complicating endovascular aneurysm repair. Occlusion of the hypogastric arteries (HAs) during endovascular repair of aortoiliac aneurysms (AIAs) results in a significant incidence of buttock claudication, and has been suggested as a causative factor in the development of postprocedural colonic ischemia, in addition to factors such as systemic hypotension, embolization of atheromatous debris, and interruption of inferior mesenteric artery inflow. To analyze the relationship between perioperative HA occlusion and postoperative ischemic colitis, we reviewed our experience over 2 years with Food and Drug Administration–approved endovascular graft devices for treatment of AIAs.MethodsElective repair of AIAs with bifurcated endovascular grafts was performed in 233 patients over a 2-year period. These included 184 AneuRx grafts, 17 Ancure grafts, and 32 Excluder grafts. During the experience, 44 patients (18.9%) underwent unilateral perioperative HA occlusion (28 right, 16 left) during the course of endovascular AIA repair, and 1 patient (0.4%) underwent bilateral HA occlusion.ResultsIn 4 patients (1.7%) signs and symptoms of ischemic colitis developed 2.0 ± 1.4 days postoperatively. In all patients the diagnosis was confirmed at sigmoidoscopy, and initial treatment included bowel rest, hydration, and intravenous antibiotic agents. Three patients with bilateral patent HAs required colonic resection 14.7 ± 9.7 days after the initial diagnosis, and 2 of these 3 patients died in the postoperative period. Pathologic findings confirmed the presence of atheroemboli in the colonic vasculature in all 3 patients who underwent colonic resection. The fourth patient had undergone multiple manipulations of the left HA in an unsuccessful attempt to preserve patency of this vessel during AIA repair. This patient recovered completely with nonoperative management. Perioperative unilateral HA occlusion was not associated with a significantly higher incidence of postoperative ischemic colitis.ConclusionPerioperative HA occlusion during aortoiliac open or endovascular surgery may contribute to development of the rare but potentially lethal complication of ischemic colitis. However, our extensive experience suggests that embolization of atheromatous debris to the HA tissue beds during endovascular manipulations, rather than proximal HA occlusion, is the primary cause of clinically significant ischemic colitis after endovascular aneurysm repair

Single-molecule RNA detection at depth via hybridization chain reaction and tissue hydrogel embedding and clearing

Accurate and robust detection of mRNA molecules in thick tissue samples can reveal gene expression patterns in single cells within their native environment. Preserving spatial relationships while accessing the transcriptome of selected cells is a crucial feature for advancing many biological areas, from developmental biology to neuroscience. However, because of the high autofluorescence background of many tissue samples, it is difficult to detect single-molecule fluorescence in situ hybridization (smFISH) signals robustly in opaque thick samples. Here, we draw on principles from the emerging discipline of dynamic nucleic acid nanotechnology to develop a robust method for multi-color, multi-RNA, imaging in deep tissues using single-molecule hybridization chain reaction (smHCR). Using this approach, single transcripts can be imaged using epifluorescence, confocal or selective plane illumination microscopy (SPIM) depending on the imaging depth required. We show that smHCR has high sensitivity in detecting mRNAs in cell culture and whole-mount zebrafish embryos, and that combined with SPIM and PACT (PAssive CLARITY Technique) tissue hydrogel embedding and clearing, smHCR can detect single mRNAs deep within thick (0.5 mm) brain slices. By simultaneously achieving ∼20-fold signal amplification and diffraction-limited spatial resolution, smHCR offers a robust and versatile approach for detecting single mRNAs in situ, including in thick tissues where high background undermines the performance of unamplified smFISH

Lrp4 Modulates Extracellular Integration of Cell Signaling Pathways in Development

The extent to which cell signaling is integrated outside the cell is not currently appreciated. We show that a member of the low-density receptor-related protein family, Lrp4 modulates and integrates Bmp and canonical Wnt signalling during tooth morphogenesis by binding the secreted Bmp antagonist protein Wise. Mouse mutants of Lrp4 and Wise exhibit identical tooth phenotypes that include supernumerary incisors and molars, and fused molars. We propose that the Lrp4/Wise interaction acts as an extracellular integrator of epithelial-mesenchymal cell signaling. Wise, secreted from mesenchyme cells binds to BMP's and also to Lrp4 that is expressed on epithelial cells. This binding then results in the modulation of Wnt activity in the epithelial cells. Thus in this context Wise acts as an extracellular signaling molecule linking two signaling pathways. We further show that a downstream mediator of this integration is the Shh signaling pathway