Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page

Tree block coordinate descent for map in graphical models

abstract URL: http://jmlr.csail.mit.edu/proceedings/papers/v5/sontag09a.htmlA number of linear programming relaxations have been proposed for finding most likely settings of the variables (MAP) in large probabilistic models. The relaxations are often succinctly expressed in the dual and reduce to different types of reparameterizations of the original model. The dual objectives are typically solved by performing local block coordinate descent steps. In this work, we show how to perform block coordinate descent on spanning trees of the graphical model. We also show how all of the earlier dual algorithms are related to each other, giving transformations from one type of reparameterization to another while maintaining monotonicity relative to a common objective function. Finally, we quantify when the MAP solution can and cannot be decoded directly from the dual LP relaxation

Appearance concerns in later life: Do they really exist?

In Western society, where youth and beauty are given high status, older people can often feel pressured to adopt appearance-enhancing strategies, such as using anti-ageing products. Those who invest time and money into their image often do so to show they are coping well with later life and gain respect from others. Claire Hamlet examines the concept of successful ageing in relation to appearanc

HIV stigma in UK press reporting of a case of intentional HIV transmission

The UK has set itself the ambitious target of zero new HIV transmissions by 2030. HIV stigma is a significant barrier to achieving this target. Media reporting plays an important role in shaping social representations of HIV and of stigma. Between 2016 and 2018, the media in the UK reported on the Daryll Rowe case – the first criminal prosecution for intentional transmission of HIV in the UK. This article examines the way that UK newspapers reported this case, which may have exacerbated HIV stigma. Using Nexis, 178 UK newspaper articles were extracted and subjected to qualitative thematic analysis through a social constructionist lens. Informed by social representations theory, the analysis yielded three discursive themes: (1) Representing the perpetrator through HIV-focussed metaphors; (2) Constructing volitional ambiguity; and (3) Anchoring the lived experience of HIV to misery and death. UK newspapers constructed an ‘evil vs victimhood’ dichotomy in relation to Rowe and the men infected with HIV, respectively. This article argues that news coverage of the Rowe story constructs HIV in ways that are inconsistent with public health messaging. Reporting failed to note innovations in HIV treatment and prevention but instead disseminated stigmatising social representations of HIV. This is important because stigma impedes effective HIV prevention, engagement with HIV care and ultimately our ability to achieve the zero-infections target

An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

Mechanisms and Functions of Spatial Protein Quality Control

A healthy proteome is essential for cell survival. Protein misfolding is linked to a rapidly expanding list of human diseases, ranging from neurodegenerative diseases to aging and cancer. Many of these diseases are characterized by the accumulation of misfolded proteins in intra- and extracellular inclusions, such as amyloid plaques. The clear link between protein misfolding and disease highlights the need to better understand the elaborate machinery that manages proteome homeostasis, or proteostasis, in the cell. Proteostasis depends on a network of molecular chaperones and clearance pathways involved in the recognition, refolding, and/or clearance of aberrant proteins. Recent studies reveal that an integral part of the cellular management of misfolded proteins is their spatial sequestration into several defined compartments. Here, we review the properties, function, and formation of these compartments. Spatial sequestration plays a central role in protein quality control and cellular fitness and represents a critical link to the pathogenesis of protein aggregation-linked diseases

More data means less inference: A pseudo-max approach to structured learning

The problem of learning to predict structured labels is of key importance in many applications. However, for general graph structure both learning and inference in this setting are intractable. Here we show that it is possible to circumvent this difficulty when the input distribution is rich enough via a method similar in spirit to pseudo-likelihood. We show how our new method achieves consistency, and illustrate empirically that it indeed performs as well as exact methods when sufficiently large training sets are used.United States-Israel Binational Science Foundation (Grant 2008303)Google (Firm) (Research Grant)Google (Firm) (PhD Fellowship