Semi-Supervised Single- and Multi-Domain Regression with Multi-Domain Training

We address the problems of multi-domain and single-domain regression based on distinct and unpaired labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as a Bayesian estimation with partial knowledge of statistical relations. We propose a worst-case design strategy and study the resulting estimators. Our analysis explicitly accounts for the cardinality of the labeled sets and includes the special cases in which one of the labeled sets is very large or, in the other extreme, completely missing. We demonstrate our estimators in the context of removing expressions from facial images and in the context of audio-visual word recognition, and provide comparisons to several recently proposed multi-modal learning algorithms.Comment: 24 pages, 6 figures, 2 table

Partially Linear Estimation with Application to Sparse Signal Recovery From Measurement Pairs

We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing the joint distribution of X and Y in full, but rather only its second-order moments. This renders it of potential interest in various applications. We further show that the PLMMSE method is minimax-optimal among all estimators that solely depend on the second-order statistics of X and Y. We demonstrate our approach in the context of recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version of it. We show that in this setting PLMMSE estimation has a clear computational advantage, while its performance is comparable to state-of-the-art algorithms. We apply our approach both in static and dynamic estimation applications. In the former category, we treat the problem of image enhancement from blurred/noisy image pairs, where we show that PLMMSE estimation performs only slightly worse than state-of-the art algorithms, while running an order of magnitude faster. In the dynamic setting, we provide a recursive implementation of the estimator and demonstrate its utility in the context of tracking maneuvering targets from position and acceleration measurements.Comment: 13 pages, 5 figure

Constitutive Association of Tie1 and Tie2 with Endothelial Integrins is Functionally Modulated by Angiopoietin-1 and Fibronectin

Functional cross-talk between Tie2 and Integrin signaling pathways is essential to coordinate endothelial cell adhesion and migration in response to the extracellular matrix, yet the mechanisms behind this phenomenon are unclear. Here, we examine the possibility that receptor cross-talk is driven through uncharacterized Tie-integrin interactions on the endothelial surface. Using a live cell FRET-based proximity assay, we monitor Tie-integrin receptor recognition and demonstrate that both Tie1 and Tie2 readily associate with integrins α5ß1 and αVß3 through their respective ectodomains. Although not required, Tie2-integrin association is significantly enhanced in the presence of the extracellular component and integrin ligand fibronectin. In vitro binding assays with purified components reveal that Tie-integrin recognition is direct, and further demonstrate that the receptor binding domain of the Tie2 ligand Ang-1, but not the receptor binding domain of Ang-2, can independently associate with α5ß1 or αVß3. Finally, we reveal that cooperative Tie/integrin interactions selectively stimulate ERK/MAPK signaling in the presence of both Ang-1 and fibronectin, suggesting a molecular mechanism to sensitize Tie2 to extracellular matrix. We provide a mechanistic model highlighting the role of receptor localization and association in regulating distinct signaling cascades and in turn, the angiogenic switch

Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions

We study, by incorporating short-range ion-surface interactions, ionic profiles of electrolyte solutions close to a non-charged interface between two dielectric media. In order to account for important correlation effects close to the interface, the ionic profiles are calculated beyond mean-field theory, using the loop expansion of the free energy. We show how it is possible to overcome the well-known deficiency of the regular loop expansion close to the dielectric jump, and treat the non-linear boundary conditions within the framework of field theory. The ionic profiles are obtained analytically to one-loop order in the free energy, and their dependence on different ion-surface interactions is investigated. The Gibbs adsorption isotherm, as well as the ionic profiles are used to calculate the surface tension, in agreement with the reverse Hofmeister series. Consequently, from the experimentally-measured surface tension, one can extract a single adhesivity parameter, which can be used within our model to quantitatively predict hard to measure ionic profiles.Comment: 14 pages, 6 figure

Field theory for mechanical criticality in disordered fiber networks

Strain-controlled criticality governs the elasticity of jamming and fiber networks. While the upper critical dimension of jamming is believed to be $d_u$=2, non mean-field exponents are observed in numerical studies of 2D and 3D fiber networks. The origins of this remains unclear. In this study we propose a minimal mean-field model for strain-controlled criticality of fiber networks. We then extend this to a phenomenological field theory, in which non mean-field behavior emerges as a result of the disorder in the network structure. We predict that the upper critical dimension for such systems is $d_u$=4 using a Gaussian approximation. Moreover, we identify an order parameter for the phase transition, which has been lacking for fiber networks to date

Effective Medium Theory for Mechanical Phase Transitions of Fiber Networks

Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen. These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects via an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results