Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding

Socio-demographic inequalities in stage of cancer diagnosis: Evidence from patients with female breast,lung, colon, rectal, prostate, renal, bladder, melanoma, ovarian and endometrial cancer

This is the final published version. Available from Oxford University Press via the DOI in this record.Background: Understanding socio-demographic inequalities in stage at diagnosis can inform priorities for cancer control. Patients and methods: We analysed data on the stage at diagnosis of East of England patients diagnosed with any of 10 common cancers, 2006-2010. Stage information was available on 88 657 of 98 942 tumours (89.6%). Results: Substantial socio-demographic inequalities in advanced stage at diagnosis (i.e. stage III/IV) existed for seven cancers, but their magnitude and direction varied greatly by cancer: advanced stage at diagnosis was more likely for older patients with melanoma but less likely for older patients with lung cancer [odds ratios for 75-79 versus 65-69 1.60 (1.38-1.86) and 0.83 (0.77-0.89), respectively]. Deprived patients were more likely to be diagnosed in advanced stage for melanoma, prostate, endometrial and (female) breast cancer: odds ratios (most versus least deprived quintile) from 2.24 (1.66-3.03) for melanoma to 1.31 (1.15-1.49) for breast cancer. In England, elimination of sociodemographic inequalities in stage at diagnosis could decrease the number of patients with cancer diagnosed in advanced stage by 5600 annually. Conclusions: There are substantial socio-demographic inequalities in stage at diagnosis for most cancers. Earlier detection interventions and policies can be targeted on patients at higher risk of advanced stage diagnosis. ©The Author 2012.National Institute for Health Research (NIHR

Applications of Radio-Frequency Heating in Environmental Technology

AbstractDirect dielectric heating with radio-frequency (RF) electromagnetic fields is used to optimize a variety of processes in environmental technology, namely soil remediation by soil vapor extraction or biodegradation, adsorptive-catalytic off-gas treatment, thermal regeneration of drying agents in biogas or natural gas treatment and decontamination and/or drying of brickwork

Number of HIV-1 founder variants is determined by the recency of the source partner infection

During sexual transmission, the high genetic diversity of HIV-1 within an individual is frequently reduced to one founder variant that initiates infection. Understanding the drivers of this bottleneck is crucial to developing effective infection control strategies. Little is known about the importance of the source partner during this bottleneck. To test the hypothesis that the source partner affects the number of HIV founder variants, we developed a phylodynamic model calibrated using genetic and epidemiological data on all existing transmission pairs for whom the direction of transmission and the infection stage of the source partner are known. Our results suggest that acquiring infection from someone in the acute (early) stage of infection increases the risk of multiple-founder variant transmission compared with acquiring infection from someone in the chronic (later) stage of infection. This study provides the first direct test of source partner characteristics to explain the low frequency of multiple-founder strain infections

Bell Correlations and the Common Future

Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of explaining Bell correlations through a mechanism in that spirit can be read as questioning either the principle or even its basis: causality. In the former case, the principle can be replaced by its quantum version, accepting as a common cause an entangled state, leaving the phenomenon as mysterious as ever on the classical level (on which, after all, it occurs). If, more radically, the causal structure is questioned in principle, closed space-time curves may become possible that, as is argued in the present note, can give rise to non-local correlations if to-be-correlated pieces of classical information meet in the common future --- which they need to if the correlation is to be detected in the first place. The result is a view resembling Brassard and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's relative-state formalism, avoiding "multiple realities."Comment: 8 pages, 5 figure

Relativistic Nucleus-Nucleus Collisions: from the BEVALAC to RHIC

I briefly describe the initial goals of relativistic nuclear collisions research, focusing on the LBL Bevatron/Bevalac facility in the 1970's. An early concept of high hadronic density fireball formation, and subsequent isentropic decay (preserving information as to the high density stage) led to an outline of physics observables that could determine the nuclear matter equation of state at several times nuclear ground state matter density. With the advent of QCD the goal of locating, and characterizing the hadron-parton deconfinement phase transformation suggested the need for higher $\sqrt{s}$, the research thus moving to the BNL AGS and CERN SPS, finally to RHIC at BNL. A set of physics observables is discussed where present data span the entire $\sqrt{s}$ domain, from Bevalac and SIS at GSI, to top RHIC energy. Referring, selectively, to data concerning bulk hadron production, the overall $\sqrt{s}$ evolution of directed and radial flow observables, and of pion pair Bose-Einstein correlation are discussed. The hadronization process is studied in the grand canonical statistical model. The resulting hadronization points in the plane T vs. $\mu_B$ converge onto the parton-hadron phase boundary predicted by finite $\mu_B$ lattice QCD, from top SPS to RHIC energy. At lower SPS and top AGS energy a steep strangeness maximum occurs at which the Wroblewski parameter $\lambda_s \approx$ 0.6; a possible connection to the QCD critical point is discussed. Finally the unique new RHIC physics is addressed: high $p_T$ hadron suppression and jet "tomography".Comment: 19 pages, 11 figure

Internal accounting practices at Whitbread & Company c.1890-1925

This paper examines internal accounting practices at Whitbread & Company from c. 1890 to 1925. At this time, there was an increasing interest in cost accounting, but there is little detailed extant research on general internal accounting practices of firms. The brewing sector, we suggest, is a potentially fruitful realm to further our knowledge of this time. Drawing on the Whitbread brewery archival records, we chart the internal accounting practices of the company. Our findings reveal a stable set of accounting practices, focused mainly on bookkeeping, although the firm’s auditor produced some reports which may have been useful for management decision-making. We argue these practices were highly institutionalised, and seemingly resistant to external forces present in the company’s environment

Electrical detection of magnetic skyrmions by non-collinear magnetoresistance

Magnetic skyrmions are localised non-collinear spin textures with high potential for future spintronic applications. Skyrmion phases have been discovered in a number of materials and a focus of current research is the preparation, detection, and manipulation of individual skyrmions for an implementation in devices. Local experimental characterization of skyrmions has been performed by, e.g., Lorentz microscopy or atomic-scale tunnel magnetoresistance measurements using spin-polarised scanning tunneling microscopy. Here, we report on a drastic change of the differential tunnel conductance for magnetic skyrmions arising from their non-collinearity: mixing between the spin channels locally alters the electronic structure, making a skyrmion electronically distinct from its ferromagnetic environment. We propose this non-collinear magnetoresistance (NCMR) as a reliable all-electrical detection scheme for skyrmions with an easy implementation into device architectures