Superpolynomial lower bounds for general homogeneous depth 4 arithmetic circuits

In this paper, we prove superpolynomial lower bounds for the class of homogeneous depth 4 arithmetic circuits. We give an explicit polynomial in VNP of degree $n$ in $n^2$ variables such that any homogeneous depth 4 arithmetic circuit computing it must have size $n^{\Omega(\log \log n)}$. Our results extend the works of Nisan-Wigderson [NW95] (which showed superpolynomial lower bounds for homogeneous depth 3 circuits), Gupta-Kamath-Kayal-Saptharishi and Kayal-Saha-Saptharishi [GKKS13, KSS13] (which showed superpolynomial lower bounds for homogeneous depth 4 circuits with bounded bottom fan-in), Kumar-Saraf [KS13a] (which showed superpolynomial lower bounds for homogeneous depth 4 circuits with bounded top fan-in) and Raz-Yehudayoff and Fournier-Limaye-Malod-Srinivasan [RY08, FLMS13] (which showed superpolynomial lower bounds for multilinear depth 4 circuits). Several of these results in fact showed exponential lower bounds. The main ingredient in our proof is a new complexity measure of {\it bounded support} shifted partial derivatives. This measure allows us to prove exponential lower bounds for homogeneous depth 4 circuits where all the monomials computed at the bottom layer have {\it bounded support} (but possibly unbounded degree/fan-in), strengthening the results of Gupta et al and Kayal et al [GKKS13, KSS13]. This new lower bound combined with a careful "random restriction" procedure (that transforms general depth 4 homogeneous circuits to depth 4 circuits with bounded support) gives us our final result

Simple extractors via constructions of cryptographic pseudo-random generators

Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the Blum-Micali-Yao approach) can be used for building extractors as well. Using this new technique we build extractors that do not use designs and polynomial-based error-correcting codes and that are very simple and efficient. For example, one extractor produces each output bit separately in $O(\log^2 n)$ time. These extractors work for weak sources with min entropy $\lambda n$, for arbitrary constant $\lambda > 0$, have seed length $O(\log^2 n)$, and their output length is $\approx n^{\lambda/3}$.Comment: 21 pages, an extended abstract will appear in Proc. ICALP 2005; small corrections, some comments and references adde

Legal Facts and Reasons for Action: Between Deflationary and Robust Conceptions of Law’s Reason-Giving Capacity

This chapter considers whether legal requirements can constitute reasons for action independently of the merits of the requirement at hand. While jurisprudential opinion on this question is far from uniform, sceptical views are becoming increasingly dominant. Such views typically contend that, while the law can be indicative of pre-existing reasons, or can trigger pre-existing reasons into operation, it cannot constitute new reasons. This chapter offers support to a somewhat less sceptical position, according to which the fact that a legal requirement has been issued can be a reason for action, yet one that is underpinned by bedrock values which law is apt to serve. Notions discussed here include a value-based conception of reasons as facts ; a distinction between complete and incomplete reasons ; and David Enoch’s idea of triggering reason-giving. Following a discussion of criticism against the view adopted here, the chapter concludes by considering some more ‘robust’ conceptions of law’s reason-giving capacity

Reasons, Coherence, and Group Rationality

Philosophy and Phenomenological Research, EarlyView

Retrospective observational study to assess the clinical management and outcomes of hospitalised patients with complicated urinary tract infection in countries with high prevalence of multidrug resistant Gram-negative bacteria (RESCUING)

INTRODUCTION: The emergence of multidrug resistant (MDR) Gram-negative bacteria (GNB), including carbapenemase-producing strains, has become a major therapeutic challenge. These MDR isolates are often involved in complicated urinary tract infection (cUTI), and are associated with poor clinical outcomes. The study has been designed to gain insight into the epidemiology, clinical management, outcome and healthcare cost of patients with cUTI, especially in countries with high prevalence of MDR GNB. METHODS AND ANALYSIS: This multinational and multicentre observational, retrospective study will identify cases from 1 January 2013 to 31 December 2014 in order to collect data on patients with cUTI as a cause of hospital admission, and patients who develop cUTI during their hospital stay. The primary end point will be treatment failure defined as the presence of any of the following criteria: (1) signs or symptoms of cUTI present at diagnosis that have not improved by days 5–7 with appropriate antibiotic therapy, (2) new cUTI-related symptoms that have developed within 30 days of diagnosis, (3) urine culture taken within 30 days of diagnosis, either during or after completion of therapy, that grows ≥104 colony-forming unit/mL of the original pathogen and (4) death irrespective of cause within 30 days of the cUTI diagnosis. SAMPLE SIZE: 1000 patients afford a power of 0.83 (α=0.05) to detect an absolute difference of 10% in the treatment failure rate between MDR bacteria and other pathogens. This should allow for the introduction of about 20 independent risk factors (or their interaction) in a logistic regression model looking at risk factors for failure. ETHICS AND DISSEMINATION: Approval will be sought from all relevant Research Ethics Committees. Publication of this study will be considered as a joint publication by the participating investigator leads, and will follow the recommendations of the International Committee of Medical Journal Editors (ICMJE)

Structure-based design and synthesis of antiparasitic pyrrolopyrimidines targeting pteridine reductase 1

The treatment of Human African Trypanosomiasis remains a major unmet health need in sub-Saharan Africa. Approaches involving new molecular targets are important and pteridine reductase 1 (PTR1), an enzyme that reduces dihydrobiopterin in Trypanosoma spp. has been identified as a candidate target and it has been shown previously that substituted pyrrolo[2,3-d]pyrimidines are inhibitors of PTR1 from T. brucei (J. Med. Chem. 2010, 53, 221-229). In this study, 61 new pyrrolo[2,3-d]pyrimidines have been prepared, designed with input from new crystal structures of 23 of these compounds complexed with PTR1, and evaluated in screens for enzyme inhibitory activity against PTR1 and in vitro antitrypanosomal activity. 8 compounds were sufficiently active in both screens to take forward to in vivo evaluation. Thus although evidence for trypanocidal activity in a stage I disease model in mice was obtained, the compounds were too toxic to mice for further development

Large violation of Bell inequalities with low entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order $\frac{\sqrt{n}}{\log n}$ with $n$ inputs, $n$ outputs and $n$-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the Entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.Comment: Reference [16] added. Some typos correcte

On the Computational Complexity of Measuring Global Stability of Banking Networks

Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreading of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures, define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic

Cost of hospitalised patients due to complicated urinary tract infections: a retrospective observational study in countries with high prevalence of multidrug-resistant Gram-negative bacteria: the COMBACTE-MAGNET, RESCUING study

OBJECTIVE: Complicated urinary tract infections (cUTIs) impose a high burden on healthcare systems and are a frequent cause of hospitalisation. The aims of this paper are to estimate the cost per episode of patients hospitalised due to cUTI and to explore the factors associated with cUTI-related healthcare costs in eight countries with high prevalence of multidrug resistance (MDR). DESIGN: This is a multinational observational, retrospective study. The mean cost per episode was computed by multiplying the volume of healthcare use for each patient by the unit cost of each item of care and summing across all components. Costs were measured from the hospital perspective. Patient-level regression analyses were used to identify the factors explaining variation in cUTI-related costs. SETTING: The study was conducted in 20 hospitals in eight countries with high prevalence of multidrug resistant Gram-negative bacteria (Bulgaria, Greece, Hungary, Israel, Italy, Romania, Spain and Turkey). PARTICIPANTS: Data were obtained from 644 episodes of patients hospitalised due to cUTI. RESULTS: The mean cost per case was €5700, with considerable variation between countries (largest value €7740 in Turkey; lowest value €4028 in Israel), mainly due to differences in length of hospital stay. Factors associated with higher costs per patient were: type of admission, infection source, infection severity, the Charlson comorbidity index and presence of MDR. CONCLUSIONS: The mean cost per hospitalised case of cUTI was substantial and varied significantly between countries. A better knowledge of the reasons for variations in length of stays could facilitate a better standardised quality of care for patients with cUTI and allow a more efficient allocation of healthcare resources. Urgent admissions, infections due to an indwelling urinary catheterisation, resulting in septic shock or severe sepsis, in patients with comorbidities and presenting MDR were related to a higher cost

Age-related changes in global motion coherence: conflicting haemodynamic and perceptual responses

Our aim was to use both behavioural and neuroimaging data to identify indicators of perceptual decline in motion processing. We employed a global motion coherence task and functional Near Infrared Spectroscopy (fNIRS). Healthy adults (n = 72, 18-85) were recruited into the following groups: young (n = 28, mean age = 28), middle-aged (n = 22, mean age = 50), and older adults (n = 23, mean age = 70). Participants were assessed on their motion coherence thresholds at 3 different speeds using a psychophysical design. As expected, we report age group differences in motion processing as demonstrated by higher motion coherence thresholds in older adults. Crucially, we add correlational data showing that global motion perception declines linearly as a function of age. The associated fNIRS recordings provide a clear physiological correlate of global motion perception. The crux of this study lies in the robust linear correlation between age and haemodynamic response for both measures of oxygenation. We hypothesise that there is an increase in neural recruitment, necessitating an increase in metabolic need and blood flow, which presents as a higher oxygenated haemoglobin response. We report age-related changes in motion perception with poorer behavioural performance (high motion coherence thresholds) associated with an increased haemodynamic response