Reduced spectral synthesis and compact operator synthesis

We introduce and study the notion of reduced spectral synthesis, which unifies the concepts of spectral synthesis and uniqueness in locally compact groups. We exhibit a number of examples and prove that every non-discrete locally compact group with an open abelian subgroup has a subset that fails reduced spectral synthesis. We introduce compact operator synthesis as an operator algebraic counterpart of this notion and link it with other exceptional sets in operator algebra theory, studied previously. We show that a closed subset $E$ of a second countable locally compact group $G$ satisfies reduced local spectral synthesis if and only if the subset $E^* = \{(s,t) : ts^{-1}\in E\}$ of $G\times G$ satisfies compact operator synthesis. We apply our results to questions about the equivalence of linear operator equations with normal commuting coefficients on Schatten $p$-classes.Comment: 43 page

Closable Multipliers

Let (X,m) and (Y,n) be standard measure spaces. A function f in $L^\infty(X\times Y,m\times n)$ is called a (measurable) Schur multiplier if the map $S_f$, defined on the space of Hilbert-Schmidt operators from $L_2(X,m)$ to $L_2(Y,n)$ by multiplying their integral kernels by f, is bounded in the operator norm. The paper studies measurable functions f for which $S_f$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if f is of Toeplitz type, that is, if f(x,y)=h(x-y), x,y in G, where G is a locally compact abelian group, then the closability of f is related to the local inclusion of h in the Fourier algebra A(G) of G. If f is a divided difference, that is, a function of the form (h(x)-h(y))/(x-y), then its closability is related to the "operator smoothness" of the function h. A number of examples of non-closable, norm closable and w*-closable multipliers are presented.Comment: 35 page

Episodic memory retrieval, parietal cortex, and the default mode network: Functional and topographic analyses

The default mode network (DMN) is often considered a functionally homogeneous system that is broadly associated with internally directed cognition (e.g., episodic memory, theory of mind, self-evaluation). However, few studies have examined how this network interacts with other networks during putative default processes such as episodic memory retrieval. Using functional magnetic resonance imaging, we investigated the topography and response profile of human parietal regions inside and outside the DMN, independently defined using task-evoked deactivations and resting-state functional connectivity, during episodic memory retrieval. Memory retrieval activated posterior nodes of the DMN, particularly the angular gyrus, but also more anterior and dorsal parietal regions that were anatomically separate from the DMN. The two sets of parietal regions showed different resting-state functional connectivity and response profiles. During memory retrieval, responses in DMN regions peaked sooner than non-DMN regions, which in turn showed responses that were sustained until a final memory judgment was reached. Moreover, a parahippocampal region that showed strong resting-state connectivity with parietal DMN regions also exhibited a pattern of task-evoked activity similar to that exhibited by DMN regions. These results suggest that DMN parietal regions directly supported memory retrieval, whereas non-DMN parietal regions were more involved in postretrieval processes such as memory-based decision making. Finally, a robust functional dissociation within the DMN was observed. Whereas angular gyrus and posterior cingulate/precuneus were significantly activated during memory retrieval, an anterior DMN node in medial prefrontal cortex was strongly deactivated. This latter finding demonstrates functional heterogeneity rather than homogeneity within the DMN during episodic memory retrieval

A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine

Combining insights from the study of type refinement systems and of monoidal closed chiralities, we show how to reconstruct Lawvere's hyperdoctrine of presheaves using a full and faithful embedding into a monoidal closed bifibration living now over the compact closed category of small categories and distributors. Besides revealing dualities which are not immediately apparent in the traditional presentation of the presheaf hyperdoctrine, this reconstruction leads us to an axiomatic treatment of directed equality predicates (modelled by hom presheaves), realizing a vision initially set out by Lawvere (1970). It also leads to a simple calculus of string diagrams (representing presheaves) that is highly reminiscent of C. S. Peirce's existential graphs for predicate logic, refining an earlier interpretation of existential graphs in terms of Boolean hyperdoctrines by Brady and Trimble. Finally, we illustrate how this work extends to a bifibrational setting a number of fundamental ideas of linear logic.Comment: Identical to the final version of the paper as appears in proceedings of LICS 2016, formatted for on-screen readin

Secondary electron emission from sodium chloride, glass and aluminum oxide at various temperature

The method of single impulses was used to measure the coefficients of the secondary electronic emission for 2 types of Al2O2, monocrystalline NaCl and glass at different temperatures and for different values of the energy of the primary electrons. The value of the secondary electron emission does not depend upon temperature. The effect of a gas film on the value of the secondary electron emission was detected

Noise diffraction patterns eliminated in coherent optical systems

Lens rotation technique of noise diffraction pattern elimination spreads diffracted energy, normally concentrated over small area of image, over much larger annular area. Technique advantages include simplified lens selecting process, reduced clean room requirements, and low cost equipment requirements

Behavioural clusters and predictors of performance during recovery from stroke

We examined the patterns and variability of recovery post-stroke in multiple behavioral domains. A large cohort of first time stroke patients with heterogeneous lesions was studied prospectively and longitudinally at 1-2 weeks, 3 months and one year post-injury with structural MRI to measure lesion anatomy and in-depth neuropsychological assessment. Impairment was described at all timepoints by a few clusters of correlated deficits. The time course and magnitude of recovery was similar across domains, with change scores largely proportional to the initial deficit and most recovery occurring within the first three months. Damage to specific white matter tracts produced poorer recovery over several domains: attention and superior longitudinal fasciculus II/III, language and posterior arcuate fasciculus, motor and corticospinal tract. Finally, after accounting for the severity of the initial deficit, language and visual memory recovery/outcome was worse with lower education, while the occurrence of multiple deficits negatively impacted attention recovery

The molecular structure of isocyanic acid from microwave and infra-red absorption spectra

Experimental investigations of the infra-red and microwave spectra of the slightly asymmetric rotor, HNCO, have been made, and the structure of the molecule has been determined

A preliminary review of the uses of chlorpromazine in psychiatric diseases

Amongst the recent advances in psychiatric treatmentby means of drugs, chlorpromazine is playing an ever increasing and important role. It was first used clinically by Laborit and Hugenard in 1951 in relation to anaesthetics and' later (1953) by ,Delay and Denikerl in psychiatry. It has been adopted generally for virtually every known psychiatric illness and varying opinions have been expressed concerning its efficacy. At the Oranje Hospital it has been in active use for the past 8 months with varying-sometimes startling-results. It has been tried alone or in combination with other drugs or electroconvulsive therapy (etc.)