On the BRST Operator Structure of the N=2 String

The BRST operator cohomology of $N=2$ $2d$ supergravity coupled to matter is presented. Descent equations for primary superfields of the matter sector are derived. We find one copy of the cohomology at ghost number one, two independent copies at ghost number two, and conjecture that there is a copy at ghost number three. The $N=2$ string has a twisted $N=4$ superconformal symmetry generated by the $N=2$ superstress tensor, the BRST supercurrent, the antighost superfield, and the ghost number supercurrent.Comment: 22 pages, Latex, NSF-ITP-93-17, ITP-SB-93-09, RIP-148-9

BioGlass: Physiological Parameter Estimation Using a Head-mounted Wearable Device

This work explores the feasibility of using sensors embedded in Google Glass, a head-mounted wearable device, to measure physiological signals of the wearer. In particular, we develop new methods to use Glass’s accelerometer, gyroscope, and camera to extract pulse and respiratory rates of 12 participants during a controlled experiment. We show it is possible to achieve a mean absolute error of 0.83 beats per minute (STD: 2.02) for heart rate and 1.18 breaths per minute (STD: 2.04) for respiration rate when considering different combinations of sensors. These results included testing across sitting, supine, and standing still postures before and after physical exercise

Upper endpoint estimates and extrapolation for commutators

In this note we revisit the upper endpoint estimates for commutators following the line by Harboure, Segovia and Torrea. Relying upon the suitable BMO subspace suited for the commutator that was introduced by Accomazzo, we obtain a counterpart for commutators of the upper endpoint extrapolation result by Harboure, Mac\'ias and Segovia. Multilinear counterparts are provided as well.Comment: This paper will appear in a special issue of Rev. Un. Mat. Argentina in honor of Pola Harboure. Some references were updated in this versio

Weighted norm inequalities for rough singular integral operators

In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index $B_{(n-1)/2}$. More precisely, we prove qualitative and quantitative versions of Coifman--Fefferman type inequalities and their vector-valued extensions, weighted $A_p-A_\infty$ strong and weak type inequalities for $1<p<\infty$, and $A_1-A_\infty$ type weak $(1,1)$ estimates. Moreover, Fefferman--Stein type inequalities are obtained, proving in this way a conjecture raised by the second-named author in the 90's. As a corollary, we obtain the weighted $A_1-A_\infty$ type estimates. Finally, we study rough homogenous singular integrals with a kernel involving a function $\Omega\in L^q(\mathbb{S}^{n-1})$, $1<q<\infty$, and provide Fefferman--Stein inequalities too. The arguments used for our proofs combine several tools: a recent sparse domination result by Conde--Alonso et al. \cite{CACDPO}, results by the first author in \cite{L}, suitable adaptations of Rubio de Francia algorithm, the extrapolation theorems for $A_{\infty}$ weights \cite{CMP,CGMP} and ideas contained in previous works by A. Seeger in \cite{S} and D. Fan and S. Sato \cite{FS}.Juan de la Cierva - Formaci\'on 2015 FJCI-2015-24547. BBVA Foundatio

Vector-valued operators, optimal weighted estimates and the CpC_p condition

In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to other operators and to their vector-valued extensions. Some of those results rely upon sparse domination results that in some cases we provide as well. We will also provide sharp weighted estimates for vector valued extensions relying on those sparse domination results.UNLP 11/X752 and PICT 2014-1771 ANPCYT, Argentina. Juan de la Cierva - Formaci\'on 2015 FJCI-2015-24547. CONICET PIP 11220130100329CO, Argentina

Observations on the Topological Structure in 2d Gravity Coupled to Minimal Matter

By using a bosonization we uncover the topological gravity structure of Labastida, Pernici and Witten in ordinary $2d$ gravity coupled to $(p,q)$ minimal models. We study the cohomology class associated with the fermionic charge of the topological gravity which is shown to be isomorphic to that of the total $BRST$ charge. One of the ground ring generators of $c_M <1$ string theory is found to be in the equivariant cohomology of this fermionic charge.Comment: 13 pages, plain tex, UG-5/94 Some clarifying statements and two new references adde

Regulation of Phosphorylation of Dopamine D3 Receptors in Mouse Striatal Neurons in vivo

Neuroscience - Vision and Functional Brain Imaging Poster SessionIntroduction: Dopamine D3 receptors (D3Rs) are G-protein-coupled receptors. These D3Rs inhibit adenylyl cyclase and the downstream formation of cAMP. Due to their preferential expression in the mesolimbic areas, especially in the nucleus accumbens (NAc), they are known to play a major role in the mesolimbic function. Recently, we found that D3Rs are phosphorylated at serine 229 (Ser229) by Ca2+/calmodulin-dependent protein kinase II (CaMKII). This phosphorylation is subject to the modulation, and the phosphorylation level controls receptor function. In this study, an effort was made to develop a phospho- and site-specific antibody. Using this antibody, we hypothesized that the modulation of D3R phosphorylation at Ser229 by dopamine D1 receptors would occur in the mouse NAc in vivo. Methods: To detect phosphorylation of D3Rs at Ser229 in striatal neurons in vivo, we developed a phospho- and site-specific antibody. A short peptide containing phospho-Ser229 (KRILTRQNpSQCISI) was synthesized and used as an immunogen for producing a polyclonal antibody from rabbits. Upon demonstration of the selectivity of this antibody, we used it in Western blot to monitor changes in Ser229 phosphorylation in striatal neurons in response to dopamine D1 receptor stimulation by a D1 selective agonist SKF81297. Following IACUC approval, adult male mice (CL57/BL6) were randomly divided into 2 groups (n = 3 per group). The animals received an intraperitoneal injection of saline or SKF81297 (1 mg/kg). Animals were sacrificed by cervical dislocation 15 min after drug injection. The NAc was removed and homogenized. Homogenates were centrifuged (1000 g, 10 min), and the supernatant was used for Western blot. Densities of immunoblots were measured using optical scanning and the data were analyzed using Student's t-test (p < 0.05). Results: A series of control experiments validated the selectivity of the antibody against phosphorylated D3Rs at Ser229 (pD3R-Ser229). Using this antibody, we found that the level of pD3R-Ser229 in the NAc was significantly increased in mice treated with a systemic injection of the D1 receptor agonist SKF81297 (1 mg/kg, 15 min) compared to mice treated with saline. Conclusion: Using a phospho- and site-specific antibody against phospho-D3Rs at Ser229, we found that stimulation of dopamine D1 receptors increases phosphorylation of D3Rs in the mouse NAc in vivo. Discussion: Developing a phospho- and site-specific antibody is necessary for detecting changes in D3R phosphorylation in vivo. Using this newly acquired antibody, we found that Ser229 phosphorylation of D3Rs is subject to the modulation by dopamine D1 receptors. This seems to indicate a previously-unrecognized D1-dependent negative feedback control of D3R function given that Ser229 phosphorylation inhibits D3Rs1. In a subpopulation of striatal neurons that co-express D3Rs and D1 receptors, dopamine is able to concurrently enhance the D1-mediated phosphorylation of D3Rs to induce a heterologous desensitization of D3Rs after their activation. This regulation is deemed important for maintaining normal homeostasis of D3R function and could be altered to contribute to various neurological disorders

TOPOLOGICAL MATTER, MIRROR SYMMETRY AND NON-CRITICAL (SUPER)STRINGS

We study the realization of the (super) conformal topological symmetry in two-dimensional field theories. The mirror automorphism of the topological algebra is represented as a reflection in the space of fields. As a consequence, a double BRST structure for topological matter theories is found. It is shown that the implementation of the topological symmetry in non-critical (super)string theories depends on the matter content of the two realizations connected by the mirror transformation.Comment: 45 pages, phyzzx, no figure

cM<1c_M<1 String Theory as a Constrained Topological Sigma Model

It has been argued by Ishikawa and Kato that by making use of a specific bosonization, $c_M=1$ string theory can be regarded as a constrained topological sigma model. We generalize their construction for any $(p,q)$ minimal model coupled to two dimensional (2d) gravity and show that the energy--momentum tensor and the topological charge of a constrained topological sigma model can be mapped to the energy--momentum tensor and the BRST charge of $c_M<1$ string theory at zero cosmological constant. We systematically study the physical state spectrum of this topological sigma model and recover the spectrum in the absolute cohomology of $c_M<1$ string theory. This procedure provides us a manifestly topological representation of the continuum Liouville formulation of $c_M<1$ string theory.Comment: 12 pages, Latex file, UG-9/9