Network Lasso: Clustering and Optimization in Large Graphs

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the \emph{network lasso}, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular - binary classification, predicting housing prices, and event detection in time series data - comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems

Phase diagrams of the 2D t-t'-U Hubbard model from an extended mean field method

It is well-known from unrestricted Hartree-Fock computations that the 2D Hubbard model does not have homogeneous mean field states in significant regions of parameter space away from half filling. This is incompatible with standard mean field theory. We present a simple extension of the mean field method that avoids this problem. As in standard mean field theory, we restrict Hartree-Fock theory to simple translation invariant states describing antiferromagnetism (AF), ferromagnetism (F) and paramagnetism (P), but we use an improved method to implement the doping constraint allowing us to detect when a phase separated state is energetically preferred, e.g. AF and F coexisting at the same time. We find that such mixed phases occur in significant parts of the phase diagrams, making them much richer than the ones from standard mean field theory. Our results for the 2D t-t'-U Hubbard model demonstrate the importance of band structure effects.Comment: 6 pages, 5 figure

Prazosin during threat discrimination boosts memory of the safe stimulus

The α-1 adrenoreceptor antagonist prazosin has shown promise in the treatment of post-traumatic stress disorder (PTSD) symptoms, but its mechanisms are not well understood. Here we administered prazosin or placebo prior to threat conditioning (day 1) and tested subsequent extinction (day 2) and reextinction (day 3) in healthy human participants. Prazosin did not affect threat conditioning but augmented stimulus discrimination during extinction and reextinction, via lower responding to the safe stimulus. These results suggest that prazosin during threat acquisition may have influenced encoding or consolidation of safety processing in particular, subsequently leading to enhanced discrimination between the safe and threatening stimuli

Online public services access and the elderly : assessing determinants of behaviour in the UK and Japan

The present study examines three research questions. Firstly, what are the critical personal factors that impact on the technology readiness of elderly people? Personal factors relate to the capability of elderly people which might affect their attitudes towards online public services access. Secondly, what are the critical social factors that impact on the technology readiness of elderly people? Elderly people’s attitudes towards social interaction may impact on their willingness to interact through online channels. The third research question explores whether personal or social factors have a greater impact on the technology readiness of elderly people and their behavioural intention towards online public services? Although technology readiness has been recognized as a factor in promoting behavioural intention toward high-tech products or services, the question of the impact of elderly people’s technology readiness on their behavioural intention toward online public services requires exploration

The BCS Functional for General Pair Interactions

The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.Comment: Revised Version. To appear in Commun. Math. Phys

Herschel/HIFI deepens the circumstellar NH3 enigma

Circumstellar envelopes (CSEs) of a variety of evolved stars have been found to contain ammonia (NH3) in amounts that exceed predictions from conventional chemical models by many orders of magnitude. The observations reported here were performed in order to better constrain the NH3 abundance in the CSEs of four, quite diverse, oxygen-rich stars using the NH3 ortho J_K = 1_0 - 0_0 ground-state line. We used the Heterodyne Instrument for the Far Infrared aboard Herschel to observe the NH3 J_K = 1_0 - 0_0 transition near 572.5 GHz, simultaneously with the ortho-H2O J_Ka,Kc = 1_1,0 -1_0,1 transition, toward VY CMa, OH 26.5+0.6, IRC+10420, and IK Tau. We conducted non-LTE radiative transfer modeling with the goal to derive the NH3 abundance in these objects' CSEs. For the latter two stars, Very Large Array imaging of NH3 radio-wavelength inversion lines were used to provide further constraints, particularly on the spatial extent of the NH3-emitting regions. Results. We find remarkably strong NH3 emission in all of our objects with the NH3 line intensities rivaling those obtained for the ground state H2O line. The NH3 abundances relative to H2 are very high and range from 2 x 10-7 to 3 x 10-6 for the objects we have studied. Our observations confirm and even deepen the circumstellar NH3 enigma. While our radiative transfer modeling does not yield satisfactory fits to the observed line profiles, it leads to abundance estimates that confirm the very high values found in earlier studies. New ways to tackle this mystery will include further Herschel observations of more NH3 lines and imaging with the Expanded Very Large Array.Comment: 4+2 page

Single-cell alternative polyadenylation analysis delineates GABAergic neuron types.

BACKGROUND: Alternative polyadenylation (APA) is emerging as an important mechanism in the post-transcriptional regulation of gene expression across eukaryotic species. Recent studies have shown that APA plays key roles in biological processes, such as cell proliferation and differentiation. Single-cell RNA-seq technologies are widely used in gene expression heterogeneity studies; however, systematic studies of APA at the single-cell level are still lacking. RESULTS: Here, we described a novel computational framework, SAPAS, that utilizes 3'-tag-based scRNA-seq data to identify novel poly(A) sites and quantify APA at the single-cell level. Applying SAPAS to the scRNA-seq data of phenotype characterized GABAergic interneurons, we identified cell type-specific APA events for different GABAergic neuron types. Genes with cell type-specific APA events are enriched for synaptic architecture and communications. In further, we observed a strong enrichment of heritability for several psychiatric disorders and brain traits in altered 3' UTRs and coding sequences of cell type-specific APA events. Finally, by exploring the modalities of APA, we discovered that the bimodal APA pattern of Pak3 could classify chandelier cells into different subpopulations that are from different laminar positions. CONCLUSIONS: We established a method to characterize APA at the single-cell level. When applied to a scRNA-seq dataset of GABAergic interneurons, the single-cell APA analysis not only identified cell type-specific APA events but also revealed that the modality of APA could classify cell subpopulations. Thus, SAPAS will expand our understanding of cellular heterogeneity