Algorithms and literate programs for weighted low-rank approximation with missing data

Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets

Normal forms and entanglement measures for multipartite quantum states

A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence and the 3-tangle), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover a natural extension of the definition of GHZ-states to e.g. $2\times 2\times N$ systems is obtained.Comment: Proof of uniqueness of normal form adde

Identification method based on Zadeh filter models

Mathematical modeling which provides the description of objects and proper organization of control operations in future is an integral stage in the automation of production. One of the approaches to build a mathematical model of an object is to represent nonlinear systems as combinations of inertial and nonlinear inertialess elements. The models thus obtained are called block-oriented. In this paper, we consider nonlinear dynamic objects represented as the models of the Zadeh filter class. In the process of the method development the identification equations were derived for the case when the test signal is a single sinusoid. Then the case of two sinusoids was considered. Such investigations allowed us to identify the patterns and describe the general case for several test components in the signal. The results of digital modeling using the sum of harmonic signals confirm the feasibility and validity of the proposed approach for identifying nonlinear models of the Zadeh filter class

The relation between self-event connections and personality functioning in youth with severe psychopathology

OBJECTIVE: One way in which individuals construct their narrative identity is by making self‐event connections, which are often linked to better functioning. Being unable to make connections is related to identity discontinuity and psychopathology. Work in the general population corroborates this association, but also highlights the importance of focusing on specific aspects of these connections and on vulnerable populations. METHOD: We examined the association of self‐event connections with personality functioning in youth with severe psychopathology (cross‐sectional N = 228, M (age) = 19.5, longitudinal N = 84), and the role of event and connection valence in the subsample of youth who made a connection (n = 188 and n = 68). Negative affectivity was controlled for in all models. RESULTS: We found no evidence that self‐event connections, nor connection valence and its interaction with event valence, are related to functioning. Positive event valence was associated with better functioning. Higher negative affectivity was strongly linked to lower functioning and explained the relation between event valence and functioning. No longitudinal associations emerged. CONCLUSIONS: These findings show that for youth with severe psychopathology making self‐event connections may not be associated with better functioning. Moreover, negative affectivity may be a distal predictor of both event valence and functioning

Neural precursors of future liking and affective reciprocity

Why do certain group members end up liking each other more than others? How does affective reciprocity arise in human groups? The prediction of interpersonal sentiment has been a long-standing pursuit in the social sciences. We combined fMRI and longitudinal social network data to test whether newly acquainted group members’ reward-related neural responses to images of one another’s faces predict their future interpersonal sentiment, even many months later. Specifically, we analyze associations between relationship-specific valuation activity and relationship-specific future liking. We found that one’s own future (T2) liking of a particular group member is predicted jointly by actor’s initial (T1) neural valuation of partner and by that partner’s initial (T1) neural valuation of actor. These actor and partner effects exhibited equivalent predictive strength and were robust when statistically controlling for each other, both individuals’ initial liking, and other potential drivers of liking. Behavioral findings indicated that liking was initially unreciprocated at T1 yet became strongly reciprocated by T2. The emergence of affective reciprocity was partly explained by the reciprocal pathways linking dyad members’ T1 neural data both to their own and to each other’s T2 liking outcomes. These findings elucidate interpersonal brain mechanisms that define how we ultimately end up liking particular interaction partners, how group members’ initially idiosyncratic sentiments become reciprocated, and more broadly, how dyads evolve. This study advances a flexible framework for researching the neural foundations of interpersonal sentiments and social relations that—conceptually, methodologically, and statistically—emphasizes group members’ neural interdependence

Sodium-dependent phosphate transporters in osteoclast differentiation and function.

Osteoclasts are multinucleated bone degrading cells. Phosphate is an important constituent of mineralized bone and released in significant quantities during bone resorption. Molecular contributors to phosphate transport during the resorptive activity of osteoclasts have been controversially discussed. This study aimed at deciphering the role of sodium-dependent phosphate transporters during osteoclast differentiation and bone resorption. Our studies reveal RANKL-induced differential expression of sodium-dependent phosphate transport protein IIa (NaPi-IIa) transcript and protein during osteoclast development, but no expression of the closely related NaPi-IIb and NaPi-IIc SLC34 family isoforms. In vitro studies employing NaPi-IIa-deficient osteoclast precursors and mature osteoclasts reveal that NaPi-IIa is dispensable for bone resorption and osteoclast differentiation. These results are supported by the analysis of structural bone parameters by high-resolution microcomputed tomography that yielded no differences between adult NaPi-IIa WT and KO mice. By contrast, both type III sodium-dependent phosphate transporters Pit-1 and Pit-2 were abundantly expressed throughout osteoclast differentiation, indicating that they are the relevant sodium-dependent phosphate transporters in osteoclasts and osteoclast precursors. We conclude that phosphate transporters of the SLC34 family have no role in osteoclast differentiation and function and propose that Pit-dependent phosphate transport could be pivotal for bone resorption and should be addressed in further studies