Easiness Amplification and Uniform Circuit Lower Bounds

We present new consequences of the assumption that time-bounded algorithms can be "compressed" with non-uniform circuits. Our main contribution is an "easiness amplification" lemma for circuits. One instantiation of the lemma says: if n^{1+e}-time, tilde{O}(n)-space computations have n^{1+o(1)} size (non-uniform) circuits for some e > 0, then every problem solvable in polynomial time and tilde{O}(n) space has n^{1+o(1)} size (non-uniform) circuits as well. This amplification has several consequences: * An easy problem without small LOGSPACE-uniform circuits. For all e > 0, we give a natural decision problem, General Circuit n^e-Composition, that is solvable in about n^{1+e} time, but we prove that polynomial-time and logarithmic-space preprocessing cannot produce n^{1+o(1)}-size circuits for the problem. This shows that there are problems solvable in n^{1+e} time which are not in LOGSPACE-uniform n^{1+o(1)} size, the first result of its kind. We show that our lower bound is non-relativizing, by exhibiting an oracle relative to which the result is false. * Problems without low-depth LOGSPACE-uniform circuits. For all e > 0, 1 < d < 2, and e < d we give another natural circuit composition problem computable in tilde{O}(n^{1+e}) time, or in O((log n)^d) space (though not necessarily simultaneously) that we prove does not have SPACE[(log n)^e]-uniform circuits of tilde{O}(n) size and O((log n)^e) depth. We also show SAT does not have circuits of tilde{O}(n) size and log^{2-o(1)}(n) depth that can be constructed in log^{2-o(1)}(n) space. * A strong circuit complexity amplification. For every e > 0, we give a natural circuit composition problem and show that if it has tilde{O}(n)-size circuits (uniform or not), then every problem solvable in 2^{O(n)} time and 2^{O(sqrt{n log n})} space (simultaneously) has 2^{O(sqrt{n log n})}-size circuits (uniform or not). We also show the same consequence holds assuming SAT has tilde{O}(n)-size circuits. As a corollary, if n^{1.1} time computations (or O(n) nondeterministic time computations) have tilde{O}(n)-size circuits, then all problems in exponential time and subexponential space (such as quantified Boolean formulas) have significantly subexponential-size circuits. This is a new connection between the relative circuit complexities of easy and hard problems

On the (Non) NP-Hardness of Computing Circuit Complexity

The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function f and a size parameter k, is the circuit complexity of f at most k? This is the definitive problem of circuit synthesis, and it has been studied since the 1950s. Unlike many problems of its kind, MCSP is not known to be NP-hard, yet an efficient algorithm for this problem also seems very unlikely: for example, MCSP in P would imply there are no pseudorandom functions. Although most NP-complete problems are complete under strong "local" reduction notions such as poly-logarithmic time projections, we show that MCSP is provably not NP-hard under O(n^(1/2-epsilon))-time projections, for every epsilon > 0. We prove that the NP-hardness of MCSP under (logtime-uniform) AC0 reductions would imply extremely strong lower bounds: NP notsubset P/poly and E notsubset i.o.-SIZE(2^(delta * n)) for some delta > 0 (hence P = BPP also follows). We show that even the NP-hardness of MCSP under general polynomial-time reductions would separate complexity classes: EXP != NP cap P/poly, which implies EXP != ZPP. These results help explain why it has been so difficult to prove that MCSP is NP-hard. We also consider the nondeterministic generalization of MCSP: the Nondeterministic Minimum Circuit Size Problem (NMCSP), where one wishes to compute the nondeterministic circuit complexity of a given function. We prove that the Sigma_2 P-hardness of NMCSP, even under arbitrary polynomial-time reductions, would imply EXP notsubset P/poly

Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems

A frontier open problem in circuit complexity is to prove P^{NP} is not in SIZE[n^k] for all k; this is a necessary intermediate step towards NP is not in P_{/poly}. Previously, for several classes containing P^{NP}, including NP^{NP}, ZPP^{NP}, and S_2 P, such lower bounds have been proved via Karp-Lipton-style Theorems: to prove C is not in SIZE[n^k] for all k, we show that C subset P_{/poly} implies a "collapse" D = C for some larger class D, where we already know D is not in SIZE[n^k] for all k. It seems obvious that one could take a different approach to prove circuit lower bounds for P^{NP} that does not require proving any Karp-Lipton-style theorems along the way. We show this intuition is wrong: (weak) Karp-Lipton-style theorems for P^{NP} are equivalent to fixed-polynomial size circuit lower bounds for P^{NP}. That is, P^{NP} is not in SIZE[n^k] for all k if and only if (NP subset P_{/poly} implies PH subset i.o.- P^{NP}_{/n}). Next, we present new consequences of the assumption NP subset P_{/poly}, towards proving similar results for NP circuit lower bounds. We show that under the assumption, fixed-polynomial circuit lower bounds for NP, nondeterministic polynomial-time derandomizations, and various fixed-polynomial time simulations of NP are all equivalent. Applying this equivalence, we show that circuit lower bounds for NP imply better Karp-Lipton collapses. That is, if NP is not in SIZE[n^k] for all k, then for all C in {Parity-P, PP, PSPACE, EXP}, C subset P_{/poly} implies C subset i.o.-NP_{/n^epsilon} for all epsilon > 0. Note that unconditionally, the collapses are only to MA and not NP. We also explore consequences of circuit lower bounds for a sparse language in NP. Among other results, we show if a polynomially-sparse NP language does not have n^{1+epsilon}-size circuits, then MA subset i.o.-NP_{/O(log n)}, MA subset i.o.-P^{NP[O(log n)]}, and NEXP is not in SIZE[2^{o(m)}]. Finally, we observe connections between these results and the "hardness magnification" phenomena described in recent works

Neuropathologic basis of frontotemporal dementia in progressive supranuclear palsy.

BackgroundProgressive supranuclear palsy (PSP) is a neurodegenerative disorder characterized by neuronal loss in the extrapyramidal system with pathologic accumulation of tau in neurons and glia. The most common clinical presentation of PSP, referred to as Richardson syndrome, is that of atypical parkinsonism with vertical gaze palsy, axial rigidity, and frequent falls. Although cognitive deficits in PSP are often ascribed to subcortical dysfunction, a subset of patients has dementia with behavioral features similar to the behavioral variant of frontotemporal dementia. In this study we aimed to identify the clinical and pathological characteristics of PSP presenting with frontotemporal dementia.MethodsIn this study, we compared clinical and pathologic characteristics of 31 patients with PSP with Richardson syndrome with 15 patients with PSP with frontotemporal dementia. For pathological analysis, we used semiquantitative methods to assess neuronal and glial lesions with tau immunohistochemistry, as well image analysis of tau burden using digital microscopic methods.ResultsWe found greater frontal and temporal neocortical neuronal tau pathology in PSP with frontotemporal dementia compared with PSP with Richardson syndrome. White matter tau pathology was also greater in PSP with frontotemporal dementia than PSP with Richardson syndrome. Genetic and demographic factors were not associated with atypical distribution of tau pathology in PSP with frontotemporal dementia.ConclusionsThe results confirm the subset of cognitive-predominant PSP mimicking frontotemporal dementia in PSP. PSP with frontotemporal dementia has distinct clinical features that differ from PSP with Richardson syndrome, as well as differences in distribution and density of tau pathology. © 2019 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society

Use of Bacteriocins to Improve Cheese Quality and Safety

End of Project ReportThe objectives of this project were to generate, characterise and exploit a range of novel bacteriocin producing starter cultures to improve both the safety and the quality of fermented dairy foods. The main conclusions were as follows: Lacticin 3147 is a broad spectrum bacteriocin which inhibits a wide range of Gram-positive bacteria including lactobacilli, clostridia and Listeria. The bacteriocin has been purified by chromatographic procedures and has been shown to be composed of two peptides, both of which are required for biological activity. The mechanism of action of lacticin 3147 has been elucidated. The entire plasmid encoding lacticin 3147 has been sequenced and the bacteriocin in distinct from any previously characterised lactococcal bacteriocin. The Food Grade introduction of the bacteriocin genes into cheese starters was carried out. Lacticin 3147 producing starters have been used to control the pathogen Listeria monocytogenes on the surface of mould ripened cheese. Lacticin 3147 producing starters have been used to control the non-starter lactic acid bacteria complement in Cheddar cheese during the ripening process. A novel starter system using a bacteriocin (lactococcin)- producing adjunct has been designed which gives increased cell lysis during Cheddar cheese manufacture while ensuring that efficient acid production is not compromised. In summary these studies have found that naturally occurring antimicrobials such as bacteriocins have a wide range of applications in the food industry for improving both the quality and safety of fermented dairy products.Department of Agriculture, Food and the Marin

A conference management system with verified document confidentiality

We present a case study in verified security for realistic systems: the implementation of a conference management system, whose functional kernel is faithfully represented in the Isabelle theorem prover, where we specify and verify confidentiality properties. The various theoretical and practical challenges posed by this development led to a novel security model and verification method generally applicable to systems describable as input–output automata

Invasive Pests of Landscape Trees in Utah

This guide provides an overview of the Utah First Detector Program and how to submit samples. The guide reviews the diseases and insects that affect landscape trees in Utah

Deep Chandra Observations of Abell 2199: the Interplay between Merger-Induced Gas Motions and Nuclear Outbursts in a Cool Core Cluster

We present new Chandra observations of Abell 2199 that show evidence of gas sloshing due to a minor merger, as well as impacts of the radio source, 3C 338, hosted by the central galaxy, NGC 6166, on the intracluster gas. The new data are consistent with previous evidence of a Mach 1.46 shock 100" from the cluster center, although there is still no convincing evidence for the expected temperature jump. Other interpretations of this feature are possible, but none is fully satisfactory. Large scale asymmetries, including enhanced X-ray emission 200" southwest of the cluster center and a plume of low entropy, enriched gas reaching 50" to the north of the center, are signatures of gas sloshing induced by core passage of a merging subcluster about 400 Myr ago. An association between the unusual radio ridge and low entropy gas are consistent with this feature being the remnant of a former radio jet that was swept away from the AGN by gas sloshing. A large discrepancy between the energy required to produce the 100" shock and the enthalpy of the outer radio lobes of 3C 338 suggests that the lobes were formed by a more recent, less powerful radio outburst. Lack of evidence for shocks in the central 10" indicates that the power of the jet now is some two orders of magnitude smaller than when the 100" shock was formed.Comment: 17 pages, 20 figures, accepted for publication in Ap

Association Between Cytokines and Liver Histology in Children with Nonalcoholic Fatty Liver Disease.

BackgroundReliable non-invasive markers to characterize inflammation, hepatocellular ballooning, and fibrosis in nonalcoholic fatty liver disease (NAFLD) are lacking. We investigated the relationship between plasma cytokine levels and features of NAFLD histology to gain insight into cellular pathways driving NASH and to identify potential non-invasive discriminators of NAFLD severity and pattern.MethodsCytokines were measured from plasma obtained at enrollment in pediatric participants in NASH Clinical Research Network studies with liver biopsy-proven NAFLD. Cytokines were chosen a priori as possible discriminators of NASH and its components. Minimization of Akaike Information Criterion (AIC) was used to determine cytokines retained in multivariable models.ResultsOf 235 subjects, 31% had "Definite NASH" on liver histology, 43% had "Borderline NASH", and 25% had NAFLD but not NASH. Total plasminogen activator inhibitor 1 (PAI1) and activated PAI1 levels were higher in pediatric participants with Definite NASH and with lobular inflammation. Interleukin-8 (IL-8) was higher in those with stage 3-4 fibrosis and lobular inflammation. sIL-2rα was higher in children with stage 3-4 fibrosis and portal inflammation. In multivariable analysis, PAI1 variables were discriminators of Borderline/Definite NASH, definite NASH, lobular inflammation and ballooning. IL-8 increased with steatosis and fibrosis severity; sIL-2rα increased with fibrosis severity and portal inflammation. IL-7 decreased with portal inflammation and fibrosis severity.ConclusionsPlasma cytokines associated with histology varied considerably among NASH features, suggesting promising avenues for investigation. Future, more targeted analysis is needed to identify the role of these markers in NAFLD and to evaluate their potential as non-invasive discriminators of disease severity